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Conflict and Coordination in the Provision of Public Goods: A Conceptual Analysis of Continuous and Step-Level Games Susanne Abele, Garold Stasser and Christopher Chartier Pers Soc Psychol Rev 2010 14: 385 originally published online 2 June 2010 DOI: 10.1177/1088868310368535 The online version of this article can be found at: http://psr.sagepub.com/content/14/4/385
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Conflict and Coordination in the Provision of Public Goods: A Conceptual Analysis of Continuous and Step-Level Games
Personality and Social Psychology Review 14(4) 385–401 © 2010 by the Society for Personality and Social Psychology, Inc. Reprints and permission: sagepub.com/journalsPermissions.nav DOI: 10.1177/1088868310368535 http://pspr.sagepub.com
Susanne Abele1, Garold Stasser1, and Christopher Chartier1
Abstract Conflicts between individual and collective interests are ubiquitous in social life. Experimental studies have investigated the resolution of such conflicts using public goods games with either continuous or step-level payoff functions. Game theory and social interdependence theory identify consequential differences between these two types of games. Continuous function games are prime examples of social dilemmas because they always contain a conflict between individual and collective interests, whereas step-level games can be construed as social coordination games. Step-level games often provide opportunities for coordinated solutions that benefit both the collective and the individuals. For this and other reasons, the authors conclude that one cannot safely generalize results obtained from step-level to continuous-form games (or vice versa). Finally, the authors identify specific characteristics of the payoff function in public goods games that conceptually mark the transition from a pure dilemma to a coordination problem nested within a dilemma. Keywords Conflict, Coordination, Public Good Games, Interdependence Theory, Social Dilemma The old man at the checkout desk in a local library shakes his head in resignation. His arm rests wearily on the abraded wooden counter, which is characteristic of the physical disrepair of the public library in a small town in the Midwest. “No,” he whispers, “we do not have any books to lend that came out after 2000.” A short drive to the north, the situation at another local library presents a very different picture. Community members are happily walking out of the library building with the latest DVD releases, while young parents are bringing their toddlers to an educative and enriching story hour. How can one account for such a different situation in two public libraries, located in adjacent communities? The community members of each of the two towns have solved a social dilemma in a very different way. But were they really in the same situation to begin with? This article argues for a closer look at the nature of interdependencies in situations that are called social dilemmas. Life often presents decisions between acting in one’s own individual interests and acting to benefit an organization, community, or society. Contributing time and money to support local causes such as libraries and parks is costly to the individual, but if everyone decides it is too costly to contribute, no one gains the benefit of the public facilities and services (Hardin, 1968). Reconciling individuals’ interests with public interests is a challenge for every society, and these challenges occur in many domains of life. Hence, learning how people can be
enticed to forgo individual interests for collective interest is useful for understanding social behavior and developing social policy. We argue that a closer and more differentiated look at the situation can foster the advancement of our understanding of cooperative and selfish behavior. Conflicts of individual and collective interests are commonly studied in psychology using experimental games. These games are generically referred to as social dilemmas and include both public goods games and resource dilemmas. Our analysis focuses on public goods games.1 Experimental studies have used two different classes of public goods games to study the conflict between individual and collective interests: games in which a public benefit increases as a continuous function (usually linear) of individual contributions and ones that use a step-level function that specifies a minimum level of contributions that is sufficient to provide the public benefit. A literature search with the keywords public good and social dilemma on PsycINFO revealed 87 articles published between 1974 and 2007 that used some version of a public goods game. Of these 87 articles, about half (41) used a continuous-form
1
Miami University, Oxford, OH
Corresponding Author: Susanne Abele, Miami University, Department of Psychology, 90 N. Patterson Avenue, Oxford, OH 45056 Email:
[email protected]
386 game and half (46) used a step-level game (or a minimal contributing set game, which is a form of a step-level game). None of these research articles tried to replicate findings that were obtained using one type of game with the other type. Also, none of these research articles directly compared steplevel and continuous public goods games.2 In this article, we point out why it is essential to consider the form of the function that defines the level of public benefit generated by individual contributions. We offer suggestions for improving the theoretical and ecological validity of psychological research that addresses conflicts of individual and public interests. In many reviews of the psychological literature on social dilemmas, the distinction between continuous and step-level public goods either is not made (e.g., Liebrand, Messick, & Wilke, 1992) or, when mentioned, the review does not distinguish which studies used which type of game (e.g., Komorita & Parks, 1995, 1996). In contrast, reviews in other disciplines include this distinction as an important consideration (see, e.g., Kollock, 1998; Ledyard, 1995). We argue that the conceptual differences between these games make generalizing from one type of game to the other risky. First, we outline the rationale of a public goods game and explain the distinction between a continuous and a steplevel game. Second, we contrast continuous and step-level games from two theoretical perspectives: game theory and social interdependence theory. Third, we review several areas of research that yield inconsistent findings depending on the form of the game used. Finally, we present a conceptual framework that represents continuous and step-level games as end points on a continuum. We suggest that the region between these two types of games contains intriguing theoretical and applied questions that have not been adequately explored.
Continuous and Step-Level Public Goods Games The Prisoner’s Dilemma (PD) game is familiar to most students of psychology. Two people are interdependent, and communication between the two is not possible. Both have two options; they can either cooperate or defect. If they both defect, their payoff is lower than if they both cooperate. However, both of them will get the highest payoff if they themselves defect while the other cooperates. The cooperator is worst off in case her or his opponent defects. Hence, if both cooperate, they both have an incentive to deviate from that situation, which will result in mutual defection. Although PD is based on a story that few of us (hopefully) will ever face, the nature of the interdependency modeled is not that unusual. For example, imagine two ex-lovers who both blame the other for the failure of the relationship and cannot resist recounting the many reasons the other is a bad mate. Both are invited to a party with many of their mutual friends and acquaintances. The cooperative move for them would be to
Personality and Social Psychology Review 14(4) stay away from the party. If only one of them goes to the party, she or he will have the opportunity to tell her or his version of the romantic split and gain the sympathy and support of their friends. Going to the party would be the defecting move. However, if both go to the party, the evening will be a disaster and neither will gain any sympathy points. An important element of both the ex-lovers’ dilemma and PD is that the action of one person does directly affect the other person. If one defects, the other suffers. If one of the ex-lovers goes to the party, the other is faced with two bad outcomes: not go and be reviled or go and ruin the party for everyone. The PD game can be extended to more than two persons with more than two decision options representing different levels of cooperation. These are referred to as public goods games or, often in the behavioral sciences, more generically as social dilemmas. The underlying principle of the interdependency for these games is the same as for the PD game: There is a conflict between the collective interest and the interests of each individual. The group as a whole fares best when everyone contributes their resources to a public account in a public goods game. However, regardless of others’ actions, each individual is always better off keeping her or his resources. Thus, the dilemma is between individual incentives to defect and the collective incentive to avoid the bad outcome of everyone defecting. Take, for instance, a community garden located in a city center park of a metropolitan area. The maintenance of this community garden depends on the citizens of the neighborhood. The users of the garden are better off if all of them devote effort to the maintenance of the garden. Each individual would be better off by avoiding the cost of maintenance but coming to the garden, chatting with the other users, and taking a share of the produce at harvest time. If, however, all of the neighbors decided to simply sit and chat instead of contributing to the upkeep of the garden, no public good would be provided. The community would not have any fresh produce to enjoy and the garden itself not be a pleasant place to meet and socialize. In the behavioral sciences, there are two dominant ways of implementing a public goods game (see, e.g., Komorita & Parks, 1996). In both versions, players are given an endowment of X units and decide how much of the endowment to contribute to the public good, Y (0 ≤ Y ≤ X). In a continuous function version of a public goods game, each contribution to the public account is multiplied by a factor of c and the public pool is distributed equally among the players at the end of the game. The size of c is set so that each player would be better off keeping a unit of her or his endowment than contributing it, regardless of the decisions of the other players. However, if all players keep their endowments, they are worse off than if they had contributed all of their endowments. This tension between contributing to the public good and keeping one’s endowment also holds for decisions to increase one’s contribution from Y to Y + 1 for all Y. That is, a player’s payoff is always better when contributing Y than
Abele et al. when contributing Y + 1, and thus the only stable solution for such a game is for all players to contribute nothing. To illustrate, suppose that three players are endowed with 10 resource units or points that have a value of $1 each. They individually decide how many points to contribute to a public account without knowing what the others decide. Points not contributed are kept in each player’s private account and retain their value of $1 each. Points contributed to the public account earn a 50% bonus and, thus, have a value of $1.50. The total value of the public good is distributed equally among the three players at the end of the game. Consider three possible outcomes of this game. The first case is simple: Each player keeps the endowment of 10 points and leaves with $10. Nothing is contributed to the public account and nothing is gained from the public account. In the second case, everyone contributes all of their points. As a result, the private accounts contain nothing and the public account contains 30 points, which is valued at $45. By everyone contributing everything, each receives $15 (i.e., one third of the value in the public account). Thus, everyone fares better if they all contribute all of their points than if no one contributes. In the third case, Players B and C each contribute 10 points but Player A contributes nothing. In this case the public account has 20 points and a value of $30. Thus, Player A receives $10 for the points retained in her or his private account but also gets $10 for her or his share of the public account—$20 in total. In contrast, Players B and C have nothing in their private accounts and receive only their share of the public account—$10 each. The dilemma resides in the fact that each player individually fares better by not contributing regardless of the others’ decisions. As the foregoing example illustrates, when Players B and C contribute all of their points, Player A does better by contributing nothing ($20) than by contributing her or his 10 points ($15). Indeed, Player A does better by contributing nothing regardless of what Players B and C do. However, the other two players are faced with the same contingencies and are likewise economically motivated to contribute nothing. Returning to our community garden example, the dilemma would be a continuous one if every hour worked or dollar donated by a member of the community yielded more produce at the end of the season and a more pleasant community garden. One could imagine such a situation, where the infrastructure necessary for the garden (fencing, watering equipment, benches, etc.) is already in place, perhaps from the previous year, and every hour of watering, fertilizing, weeding, and pruning increases the garden’s final value to the neighborhood. However, if the value added by an hour of work is slight, then sitting idly by waiting for others to work is a tempting option to everyone in the community. However, if no one does the work, the garden falls into disrepair and produces nothing. Everyone benefits from the efforts of others, but the value added by any one person’s effort is not sufficient to justify the effort.
387 A step-level game contains a provision point that specifies a level of contribution at which a fixed amount is added to the public good. In the standard step-level game, the contributions to the public account are lost if the total contributions fall short of the provision point. If the total contributions exceed the provision point, excess contributions are treated in one of two ways: Either nothing is gained by the excess contributions or the value of the common pool increases by a factor of c as in the continuous function game. When total contributions are near or at the provision point, it is no longer necessarily the case that a player is better off not contributing or reducing her or his contribution. If her or his contribution results in satisfying the provision point, she or he is often better off contributing than not. If the sum of the players’ contributions is exactly the provision point, there is no incentive for any one of them to reduce (or to increase) their contribution. In the standard step-level game, the provision point is defined in terms of the total contributions from all players. For example, suppose that three players were endowed with 10 points and each point in a player’s private account was worth $1. As before, each could contribute from 0 to 10 points to the public account. However, in the step-level version, any combination of contributions totaling 15 or more points would create a public good worth $22.50. If this provision point were met or exceeded, each player would receive $7.50 from the public good and $1 for each point that remained in the individual account. If fewer than 15 points were contributed, the public good would have no value, all contributions would be lost, and players would receive only $1 for each point that remained in the individual account. If our hypothetical community garden does not return the same value for every bit of work or money devoted by the citizens, the situation can be quite different. Imagine, for example, if the basic infrastructure of the garden is not yet in place and the community is starting the project from scratch. There would be some amount of resources and work required to prepare the garden for planting or community use at all. The garden may need a fence to protect the plants from encroaching wildlife and the grounds cleared of rocks and weeds before any vegetables or flowers can thrive. In this case, there is a minimum amount of work needed to make the garden a viable community resource. If one values the garden, then providing the effort that makes the difference between having no garden and having a garden can be both individually and collectively worthwhile. For example, if the community were very near reaching the goal of building the fence, contributing the remaining amount of time or money to complete the fence could be a relatively attractive option to any one community member. A variant of the step-level game is the minimal contributing set game. In a minimal contributing set game, players contribute either all or none of their endowment. The provision point is defined by the number of players who must
388 contribute to create value in the public account. Thus, the minimal contributing set game is a special case of a steplevel game. We focus our comments on the step-level game with the provision point defined by the sum of contributions. However, our conclusions about the characteristics of steplevel games apply to minimal contributing set games as well, and several of the studies that we review use minimal contributing set games. Although a step-level game and continuous function public goods game are similar in many respects, they are different in an important way. Namely, in a continuous game, an individual is invariably better off if she or he contributes less, as opposed to more. In a step-level game, this temptation to withhold or reduce contributions is not present when the group has reached the provision point. A simple thought experiment illustrates this difference. Suppose that in our foregoing example, Player A expects or knows that the other two players will contribute 5 points. This expectation in the continuous function game does not change the fact that Player A’s payoff will be higher by not contributing than by contributing. In contrast, the implications regarding what she or he should do to maximize her or his individual wealth are different in the step-level version. Her or his contribution of 5 points plus the 10 points contributed by others will satisfy the provision point of 15, and the public account will be worth $22.50. Thus, her or his 5-point contribution will be more than repaid by her or his $7.50 share of the public good.
Game Theory From a game theoretic perspective (Von Neumann & Morgenstern, 1947), these examples are a long way of illustrating two fundamental differences between continuous and steplevel public goods games (see Ledyard, 1995, for a more detailed analysis). The first difference is that the continuousform game has one Nash equilibrium whereas the step-level game has several.3 A Nash equilibrium is a theoretical concept but has important implications for behavior in interdependent decision making. Formally, a Nash equilibrium is a solution or pattern of choices in which each person’s decision is the best response to the others’ decisions. As a result, a Nash equilibrium, once it occurs, is a relatively stable solution because no one is motivated to change her or his choice. Moreover, if players fully understand the game, are motivated to maximize their individual outcomes, and assume that others also fully understand and are so motivated, they will play the Nash equilibrium, if one and only one such equilibrium exists. From a dynamical systems perspective, Nash equilibria tend to act as attractors in repeated games, in that decisions tend to move toward a Nash equilibrium over time, and once the Nash equilibrium is played there is a strong resistance for anyone to change. In the continuous form of the game, everyone contributing nothing is the only Nash equilibrium. That is, contributing nothing is not only the best
Personality and Social Psychology Review 14(4) response to others’ contributing nothing but also each player’s best response to any pattern of contributions by others. In a step-level game, contributing nothing is not always a player’s best response to the decisions of others. That is, there are multiple Nash equilibria in a step-level game. In the foregoing example of a step-level game, everyone contributing nothing is an equilibrium, but it is not the only one. Any combination of contributions that sum to the provision point is also a Nash equilibrium. Consider, for example, a case in which Player A contributes 3 points, Player B contributes 5 points, and Player C contributes 7 points to reach a provision point of 15. In the aforementioned step-level game, no player in this case would improve her or his economic outcome if she or he were to respond differently given what the other players contributed. Player C may think it is unfair that she or he is contributing more than the others. Nonetheless, she or he would receive a worse economic outcome if she or he were to give less than 7 in light of what the others have done. That is, her or his best economic response to the Players A and B giving 3 and 5, respectively, is to give 7. Another fundamental difference between step-level and continuous-form games is related to the game theoretic concept of Pareto efficiency. A pattern of decisions or a solution to a game is Pareto efficient if no other solution exists that improves at least one player’s outcome without adversely affecting someone else’s outcome. In the continuous-form game, everyone contributing everything is Pareto efficient but the Nash equilibrium—everyone contributing nothing— is not. Compared to everyone contributing nothing, there are many solutions that improve outcomes for at least one player while not adversely affecting others. One of these solutions is, of course, for everyone to contribute their entire endowment. Moreover, everyone contributing everything is the solution that maximizes the collective outcome in the sense that the group earns as much as possible. Thus, behaviorally, Pareto efficient solutions are stable solutions if players are motivated to avoid harm to others. Moreover, in the continuousform game, the motivation for the collective to earn as much as possible is satisfied by the Pareto efficient solution. In the step-level game that we described earlier, any solution that minimally satisfies the provision point is a Pareto efficient solution. For example, in the case outlined above, three players satisfy the provision point of 15 by contributing 3, 5, and 7 units. If any one of these players tried to improve her or his individual outcome by contributing less, she or he would succeed only if another player (or other players) compensated by contributing more to obtain the public good. This condition holds for any combination of decisions that minimally satisfies the provision point. To summarize, continuous-form and step-level games are different in terms of two important game theoretic concepts. In the continuous-form game, everyone contributing nothing is a Nash equilibrium but everyone contributing everything is Pareto efficient. In the step-level game, many patterns of
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Abele et al. decisions that minimally satisfy the provision point are both Nash equilibria and Pareto efficient solutions. Consequently, there is no dominant strategy for an individual in a step-level game. That is, there is no strategy that would always make her or him better off, regardless of what the others are choosing.
H F
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Social Interdependence Theory Kelley and Thibaut (1978), in their classic treatise of social interdependence theory, distinguished three components of interdependency in social relationships (also see Kelley et al., 2003). They developed their analysis primarily in terms of two-person interactions represented by 2 × 2 payoff matrices. An instructive example is the Battle of the Sexes (BOS) as represented in Figure 1. In the traditional presentation, a wife (W) and her husband (H) are deciding between going to the opera (O) and a football game (F). Stereotypically, the wife prefers O whereas the husband prefers F. However, they also prefer to attend the same event together. Thus, the solutions in which they do the same thing—(O, O) and (F, F)— are favored over solutions in which they do different things—(O, F) and (F, O). Nonetheless, W prefers (O, O) to (F, F) and H prefers (F, F) to (O, O). This example illustrates two of Kelley and Thibaut’s components of interdependency. First, each person has an individual preference that partly determines the value of each solution for each party. Kelley and Thibaut referred to this component as reflexive control (RC). RC is the degree to which a person prefers one choice independent of what others do. That is, the person’s decision directly reflects value back to her or him. Second, each person’s choice affects the values of the other’s choices. They dubbed this latter dimension behavioral control (BC) because one person’s response changes the values associated with the other person’s responses. In the BOS, there is mutual behavioral control because each person’s decision affects the payoffs associated with the other’s possible decisions. The third component in their analysis is fate control (FC). This component refers to the degree that one’s decision directly affects the outcomes of others. Pure mutual FC is illustrated in Figure 2. In this example A responding X gives B a better outcome than if A responds Y. The FC is mutual because B can likewise directly affect the outcomes of A. If B responds Y, A gets 10 points but B responding X gives A nothing. Kelley and Thibaut (1978) demonstrated that classic interdependencies such as the BOS, PD, and chicken can be represented as different mixes of RC, BC, and FC. For example, consider the aforementioned PD as depicted in Figure 3. Each person’s choice is typically labeled as cooperate (C) or defect (D). Although the BOS is a mix of RC and BC, the PD is a mix of RC and FC. The RC component produces the condition that both players will fare better by defecting (D) regardless of what the other does. The FC component is because of the fact that by responding D, a player adversely
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Figure 1. The Battle of the Sexes game
Note: Values above the diagonal refer to the column player’s outcome; values below the diagonal refer to the row player’s outcome.
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Figure 2. A coordination game with pure mutual fate control
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Figure 3. The Prisoner’s Dilemma game
affects the other’s outcome whether the other responds D or C. Moreover, the FC component is noncorrespondent relative to the RC. That is, by selecting the choice that is favored by the RC component, a player adversely affects the other’s outcome. The BC component of a BOS is experienced as a coordination game; it is mutually beneficial for the players to coordinate their decisions by selecting the same activity. In contrast,
390 the PD is experienced as a game of conflict; acting to improve one’s own outcome adversely affects the other’s outcome. Contrasting the continuous-form and step-level public goods game according to Kelley and Thibaut’s (1978) theory illustrates that the games are different in their basic components of interdependence. The continuous-form game is a mix of RC and FC with no BC. Each player prefers to contribute less rather than more, and the adverse impact of contributing one unit of her or his outcome is the same regardless of what others do (RC). However, one player’s decision to contribute a unit of resource benefits others by a specific amount regardless of what they do (FC). Thus, the continuousform public goods game, such as the PD game, directly pits RC (individual preference) against FC (the opportunity to help or harm others). The step-level game is a complex mix of RC and BC. Every player, as in the continuous form of the game, prefers to contribute less rather than more, other things being equal. However, other things are not always equal in the step-level game. The outcomes for different levels of contributions are also affected by what others do; hence, the game is characterized by BC. For example, in the game described earlier, three players have to contribute 15 points to obtain a public good worth $22.50, of which each player gets $7.50. Contrast two situations. First, suppose that two players contribute a total of 4 points. Then the third player’s best response is to contribute nothing because any amount contributed, up to and including the total endowment, would be lost. From the perspective of the third player, there is no conflict in this case because contributing nothing is the best response for herself or himself and the group. Consider a second case: The first two players contribute a total of 10 points. Now, the third player is better off contributing 5 points than contributing any other amount including nothing. Contributing 5 yields $12.50 for the 5 points left in her or his private account plus her or his share of the public good, whereas contributing nothing yields only the $10 in the private account. That is, the outcomes for contributing nothing and contributing 5 points depend on the decisions of the others. Notice also that there is no conflict in this case between her or his interests and the group’s interests. In sum, the others have BC over the third player. By recasting this example from the points of view of the other players, it is evident that the BC is mutual. In the typical step-level game, one player cannot directly affect the outcomes of others regardless of what the others do. Thus, there is no pure FC. One’s decision to contribute a unit of resource does not directly affect what others receive regardless of what they do. Rather, it may change the payoffs associated with the decisions that others make. To summarize, interdependence theory represents a continuous-form public goods game as a combination of RC and FC. Moreover, the RC and FC are noncorrespondent: Decisions that increase outcomes for the individual (RC) adversely affect outcomes for others (FC). From this
Personality and Social Psychology Review 14(4) theoretical perspective, the continuous-form public goods game is a close relative of the PD and is a game of conflict; one player’s action to protect her or his outcomes adversely affects others’ outcomes. The step-level game (as well as the minimal contributing set game) is a combination of RC and BC and, as such, is a close relative of the BOS.4 Thus, the step-level public goods game, like the BOS, is functionally a coordination game; everyone benefits if they can coordinate their decisions to minimally satisfy the provision point (Rapoport, 1987; Suleiman, Budescu, & Rapoport, 2001; van Dijk & Wilke, 1995, 2000). Nevertheless, there is the potential for conflict among individuals in how to solve the coordination problem because some prefer one stable solution over another (as in BOS).
What Do the Data Show? We have concluded that continuous and step-level public goods games are different in important ways when viewed from two prominent theoretical frameworks, game theory and social interdependence theory. However, as noted before, there are few studies that directly compare these different forms of public goods games. Nonetheless, there are several streams of research suggesting that different processes underlie people’s decisions regarding cooperation in the two types of games.
Decision Timing Consider, for instance, the timing effect in public goods games. The timing effect refers to differences in behavior depending on whether players are deciding simultaneously or pseudo-sequentially. When deciding pseudo-sequentially, players make their decision one after the other, but their decisions are not revealed to the other player or players until the game is over. Hence, the information set is the same in a pseudo-sequential and a simultaneous procedure. In either case, players do not know what others have decided when they make their choice. Abele and Ehrhart (2005), using a continuous public goods game, demonstrated that pseudosequential, compared to simultaneous, deciders are more likely to keep their endowments and less likely to reciprocate the level of contributions that they anticipate from others. Interestingly, the order of deciding in the pseudosequential, continuous game had no effect. That is, both first and second deciders exhibited less cooperation than simultaneous deciders. Effects of timing have also been observed in dilemmas with provision points. Budescu, Suleiman, and Rapoport (1995) and Budescu, Au, and Chen (1997) observed decisions in a step-level resource dilemma with a pseudo-sequential decision order.5 Their results were different from the ones observed in the continuous game: Participants who decided first requested more of the resource, and players’ requests
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Abele et al. decreased in the first three positions. Thus, the implications of the positional order effect in step-level dilemmas are quite different: They suggest that the timing cue is used as a coordination device. The nature of the decision timing effect obtained in the continuous public good game can be understood in light of the aspect that collective interests truly collide with the individual interest in that game. As collective interests become more salient and important, the likelihood of individuals choosing the alternative that yields a higher outcome for the group will increase. Moving simultaneously enhanced feelings of groupness (Abele & Ehrhart, 2005), which in turn might affect cooperation rates and the willingness to reciprocate, anticipated contributions. One explanation for the finding that simultaneous movers construed themselves and their partner more in relational terms compared to pseudo-sequential movers is that an interdependency involving a pure conflict of interests, such as the continuous public good game, may inherently trigger the concept of social interaction, regardless of the timing of decisions. That is, conflict implies social interdependence. Thus, the function of the timing cue is to vary the balance of concern for common versus individual interests. However, the nature of the effect in the step-level dilemma can be understood in light of the notion that the coordination aspect is more prevalent than the conflictual aspect of the interdependence. The situation can be construed as reaching the provision point as the main goal. In a coordination game, in which the actors primarily want to coordinate but secondarily have different preferences on how to coordinate, the actors search for whether one of them holds a position of privilege. This position of privilege could be a status marker. For example, being a man was probably perceived as having more status than being a woman in the 1940s (hence the focal point solution of “both going to the football game” in BOS). The timing of unobserved moves could be a cue for coordinating much like gender or other status markers. Treating timing as a status marker would be consistent with the findings of Budescu, Suleiman and Rapoport (1995), and Budescu, Au and Chen (1997). They observed that merely knowing the sequential timing of the decisions without knowing the decisions produces behavior patterns that are similar to those observed when earlier decisions are known to later deciders. The one who gets to choose first is entitled to a bigger share of the pie, even if decisions are unobserved. Moreover, Cooper, DeJong, Forsythe, and Ross (1993) also obtained results that are consistent with the treatment of timing as a status marker. They had participants play BOS in different timing orders, while not revealing the decision of the first mover until the second mover had made her or his choice, and found that players were more likely to coordinate on the option the first decider preferred. Hence, the implications of the timing studies in a step-level resource dilemma game parallel those obtained in BOS.
Group Size Another example in which games with a provision point yielded different results than games without a provision point is, as Weber, Kopelman, and Messick (2004) have also noted, the effect of group size. Kerr (1989) showed that perceived efficacy decreased with group size in a step-level public goods game. Perceived efficacy refers to the perceived criticality that group members ascribe to their own contributions. More specifically, it refers to the subjective probability that one’s contribution is necessary and sufficient for the group to reach the provision point. In one experiment, Kerr did indeed find that group size was per se related to cooperation rates: He observed lower rates of contributing as group size increased. Moreover, he found that perceived criticality also decreased as a function of group size. In contrast, Isaac, Walker, and Williams (1994) found the opposite effect of group size. They used a continuous public goods game and found that groups of 40 and 100 provided the public good more efficiently than groups of 4 and 10. Similarly, Carpenter (2007) found that contributions to a public pool, which grew as a linear function of members’ contributions, were significantly higher in groups of 10 than in groups of 5. Hence, when comparing the results of these studies, it could be that group size is inversely related to cooperation rates in step-level public goods games, whereas cooperation rates increase with group size in continuous public goods games. However, the studies also differed in other ways. Kerr used a one-shot game whereas Isaac et al. included multiple rounds in their experiments. Carpenter included a punishment option whereby other group members could monitor and punish free riders. These differences prompt us to look deeper at the explanations for group size effects in the two types of games. In addition to the hint that group size may have opposite effects for the two types of games, the theoretical explanations for the group size effects are different for the step-level and continuous games. Moreover, these explanations do not easily generalize from one type of game to the other. Isaac et al. (1994) attributed the increased contribution at larger group sizes in their continuous public goods games to a signaling effect, meaning that a relatively high contribution in one round should signal a willingness to contribute to other players in succeeding rounds. If such signals prompted others to reciprocate, one’s contribution at one point in time would be recouped by inducing higher contributions by others later. Moreover, for any given level of effectiveness of such signals, the anticipated benefit of signaling should increase as the number of people, whose subsequent contributions can be influenced, increases. Hence, signaling can explain the positive relationship between contributions and group size in a multitrial, continuous-form game. Consider this explanation for a multitrial, step-level game. Although it is plausible that players in a step-level game could use play
392 on one round to influence the play of others on subsequent rounds, presumably the goal of such signaling would be to realize a coordinated solution for reaching but not exceeding the provision point. Thus, increasing contributions with the goal of influencing others to contribute more in subsequent rounds makes sense only if the group has not reached the provision point. Once the provision point is reached, contributing more in the hopes of inducing others to contribute more is counterproductive. Thus, from a theoretical perspective, there is no reason to expect that group size would have the same effect in multiround step-level and continuousform games. Consider also the theoretical explanation for decreasing rates of contributions as a function of group size in one-shot, step-level games. The explanation for diminishing contributions when group size increased is that it becomes less likely that a given player will be a pivotal contributor—a contributor whose contribution is necessary for reaching the provision point. This explanation of the perceived criticality of contributions can be applied to step-level games but not to continuousform games. Consequently, a dominant explanation for the observed group size effects in step-level games does not generalize to continuous-form games. Thus, on both empirical and theoretical grounds, there are reasons to expect that the effect of group size would be different in step-level and continuous public goods games, whether the games are one shot or repeated.
Communication Communication as a means of increasing contributions has been frequently studied, and it is typically concluded that communication effects are robust (for reviews, see Ledyard, 1995; Weber et al., 2004). The explanations for the effects are varied but fall into two general types: social utility and social commitments. The social utility explanation is that communication increases the utility of collective, compared to individual, outcomes by increasing feelings of group identity or by emphasizing social norms that reinforce cooperative behavior. The social commitment explanation is that communication affords the opportunity to make explicit or implicit agreements that individuals later feel obligated to honor. For example, Orbell, Van de Kragt, and Dawes (1988) have shown that face-to-face communication increases cooperation in continuous public goods games when everyone in the group agrees to cooperate during the communication. They concluded that unanimous agreements to cooperate could either establish group identity (thereby increasing the social utility of collective outcomes) or make the commitment seem binding (i.e., a social commitment that should be honored). Similarly, Bouas and Komorita (1996) found an increase in cooperation in a continuous game when participants had the opportunity to discuss the dilemma face to face, the group experienced common fate, and participants
Personality and Social Psychology Review 14(4) perceived a high consensus favoring cooperation (also see Dawes, McTavish, & Shaklee, 1977). Although social utility and social commitment explanations apply to both continuous and step-level games, a third type of explanation, social coordination, fits only step-level games. When there is the possibility of a coordinated solution, communication can facilitate the development of a strategy for coordinating behavior (Ledyard, 1995). The social coordination explanation rests on the idea that commitments made in coordination agreements are reinforced by the structure of the step-level game. That is, once an effective coordination plan that exactly meets the provision point is realized, no one’s outcome is improved by reneging on her or his commitment. Put differently, if everybody is individually better off if a job gets done and verbal agreements specify who will do it, then it would be disadvantageous to everyone if anyone reneged on her or his agreement. Van de Kragt, Orbell, and Dawes (1983) introduced a form of step-level games, the minimal contributing set game, to study the social coordination function of communication. Indeed, all of their groups who were allowed to communicate identified who among their members would contribute to realize the public benefit and those who were designated contributors always contributed. Why? One could invoke the social utility and social commitment explanations, but Van de Kragt and colleagues noted that, once a coordinated solution was identified (i.e., who would contribute), the structure of the game served to enforce the commitments. Members of the designated minimal contributing set had better outcomes if they contributed than if they did not. Kerr and Kaufman-Gilliland (1994) and Kerr, Garst, Lewandowski, and Harris (1997) also showed that face-toface communication increased contributions in a minimal contributing set game. Kerr et al. (1997) concluded that players made commitments to cooperate in face-to-face communication and most felt obligated to honor these commitments (even when it appeared to them that their compliance could not be monitored). However, it is also the case that the participants in both studies could have made coordination agreements and reportedly did so in Kerr and Kaufman-Gilliland (1994). The important distinction between coordination agree ments and social commitments is that coordination agreements are reinforced by the interdependencies in step-level games, whereas unconditional commitments to cooperate in continuous public goods games are not. Although communication is generally thought to increase contributions, there are notable exceptions. Chen and Komorita (1994) studied communication in the form of pledges to contribute. Before each round of a five-person, continuous function public goods game, players sent each other a pledge, a statement indicating the amount each intended to contribute to the public good. When these pledges did not constrain the subsequent decision to contribute, contributions were lower than in a no-communication condition. Similarly,
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Abele et al. Wilson and Sell (1997) found that the communication of nonbinding commitments decreased cooperation in a continuous public goods game and that a considerable portion of participants pledged higher than they contributed. These studies suggest that the communication of nonbinding commitments can have adverse effects in continuous games, where there is always an incentive to contribute less. In recent studies, we directly compared communication effects in continuous, step-level, and minimal contributing set public goods games. The results support the conclusion that nonbinding commitments in the absence of face-to-face discussions have different effects for the two types of games. Like Chen and Komorita (1994), Abele, Stasser, and Chartier (2009) found that contributions declined over iterations of a continuous function public goods game and that the communication of nonbinding pledges accelerated this decline. Moreover, participants pledged more than they gave, and this discrepancy grew over interactions. In contrast and similar to Kerr and Kaufman-Gilliland (1994). it was found that nonbinding pledges increased cooperation rates in minimal contributing set games. The direct comparison of discrepancies between pledges and actual contributions in minimal contributing set and continuous games is informative. As already mentioned, this discrepancy grew larger over iterations of the continuous game, and participants were contributing about 20% of the amount that they were pledging after 10 iterations of the game. As a result, they rated each other as untrustworthy and unreliable on a postsession questionnaire. In the minimal contributing set game, the discrepancy between pledges and contributions did not grow over time and primarily occurred on trials when pledges exceeded the number needed to gain the public benefit. Thus, pledges were seemingly used as a coordination device in the minimal contributing set game, but in the continuous game they were used as an ineffective means of eliciting contributions from others. To summarize, communication increases cooperation in step-level public goods games regardless of whether the communication is face-to-face or binding. However, cooperationenhancing effects in continuous public goods games seem to occur when communication is face to face or intentions to cooperate are binding. Face-to-face communication is thought to either induce high group identity, a sense of obligation to honor commitments, or both. Our conclusion is that communication can be a means of increasing the social utility of collective outcomes and obtaining social commitment in both types of games. Moreover, communication can function as a social coordination tool in step-level games because commitments to a coordinated solution are reinforced by the payoff structure. In a continuous game, however, communication of nonbinding commitments can lead to deceptive promises to cooperate, which creates mistrust and, ultimately, low cooperation in repeated games.
Social Motives Social motives are an individual’s preferences for particular distributions of her or his own and others’ outcomes. Rather than assuming that individuals solely seek to maximize individual monetary outcomes, individual psychological costs and benefits are considered in the function of expected utility. Similarly, Kelley and Thibaut (1978) described how individual preferences can, in effect, transform the payoff matrix of a game. In this way preferences add psychological value to certain outcomes for certain individuals. An individual with a strong preference for equality may prefer that all players of a game leave with nothing over an outcome where one player gains a lot whereas others including herself or himself gain little. Although the latter outcome results in a higher individual payoff for the player in question, the value she or he places on equality in outcomes transforms the payoff such that the former is a more desirable option. Here we can see that individual differences in social motives, or preferences for particular outcomes, can transform the payoff function of the game, and with it the predicted behavior of certain players. Many social motives, commonly referred to as social value orientations (SVOs), have been identified (Messick & McClintock, 1968), but three orientations have received the vast majority of attention in social dilemma research. Individualists prefer to maximize personal outcomes, with no regard for the outcomes of others. Competitors prefer to maximize relative personal gain, or the positive difference between their own outcomes and those of others. Prosocials prefer to both maximize joint or collective outcomes as well as minimize differences between their outcomes and the outcomes of others. The impact of SVO on social dilemma behavior is widespread. Across a multitude of experimental games and applied settings, prosocials have been found to behave more cooperatively than individualists and competitors (van Lange & Liebrand, 1991). In the laboratory, prosocials compared to proselfs give more to others in coin exchange games (McClintock & Liebrand, 1988) and harvest less of a common pool in resource dilemmas (Kramer, McClintock, & Messick, 1986). Outside of the laboratory, prosocials compared to proselfs sacrifice more in personal relationships (van Lange, Agnew, Harinck, & Steemers, 1997) and donate more money to charitable causes (van Lange, Bekkers, Schuyt, & van Vugt, 2007). How do these differences in social motives affect decision making in continuous versus step-level public goods games? For simplicity we focus on two very common social motives and their corresponding SVOs. Maximizing one’s own outcomes is the most basic and a very common social motive and is said to be pursued by individualists. Maximizing joint outcomes or total gains in a group is also a very common social motive and is said to be pursued by prosocials. In a continuous game, these two motives are
394 consistently at odds. Regardless of what decision other players make, own outcomes are maximized by contributing nothing. Conversely, joint outcomes will always be maximized by contributing fully. This suggests that SVOs should have a consistent impact on contribution levels in continuous games. We found five studies that measured SVOs prior to the playing of a continuous public goods game (Chen & Bachrach, 2003; de Cremer, van Knippenberg, van Dijk, & van Leeuwen, 2008; de Cremer & van Lange, 2001; de Cremer & van Vugt, 1999; Weber & Murnighan, 2008). Although these studies manipulated several other variables, all found significant main effects of SVOs on contributions to the public good. As expected, prosocials contributed more to continuous public goods than did proselfs. In a step-level game, on the other hand, these two motives are not always at odds. In addition, neither motivation can be pursued by the same decision across all levels of contributions by other players. Let us consider several different scenarios in our three person step-level game example and then look at the decisions that would fulfill these two motives. First, suppose that two players contribute at a very low level. Because the provision point is unlikely to be reached in this situation, both personal and collective outcomes would be maximized by the third player contributing nothing. Therefore, contributing nothing is the preferred choice of both an individualist interested purely in her or his own outcome and a prosocial interested purely in collective outcomes. Alternatively, suppose that two players have contributed at a moderate level. The third player’s contribution could reach the provision point, but it would require a larger contribution than would be returned to that player by the provision of the public good. In this situation, personal outcomes would be maximized by contributing nothing, the preferred choice of a pure individualist. A pure prosocial, on the other hand, whose payoffs are transformed by a preference for collective gain, is more likely to contribute the necessary amount to reach the provision point, thus providing the public good and maximizing joint outcomes. Finally, suppose that two players have contributed at a very high level and the provision point is already reached. In this situation, any contribution by the third player would reduce both personal and joint outcomes because excess contributions to the public pool would be lost. One would expect both a pure individualist and a pure prosocial to contribute nothing to the public good.6 We can see that across these three scenarios it is not always the case that pursuing personal outcomes and pursuing joint outcomes require differential behavior. In contrast, in a continuous game, individuals pursuing these different social motives would be expected to behave differently in all possible scenarios. For these reasons, the effect of SVO on contributions should yield a different pattern of results in step-level and continuous
Personality and Social Psychology Review 14(4) dilemmas, with effects being weaker and less consistent in step-level games. We found eight studies in six articles that measured SVOs prior to the playing of a step-level public goods game (de Cremer, 2002; de Cremer & van Dijk, 2002; de Cremer & van Vugt, 1999; Offerman, Sonnemans, & Schram, 1996; Parks, 1994; Stouten, de Cremer, & van Dijk, 2005). Again, these studies manipulated many different variables, but we focus on the main effects of SVO. Two of these studies found no effect of SVO on contributions, whereas five of them did find a significant main effect of SVO. The effect sizes of these five studies were generally smaller than those of the four continuous games discussed above. Offerman et al. (1996) had participants play a 20-round game, finding a significant main effect of SVO only in the first 5 rounds of play, after which the effect was marginal. This weak effect of SVO in the later rounds of an iterated step-level public goods game may be because of changing expectations about the contributions of others. Early in the game, one may not have confident expectations about the contribution levels of others and assume an average or moderate amount of contribution, a situation that requires different decisions to maximize personal or joint outcomes. Once one has information with which to form stronger expectations of others, however, a player may find herself or himself in a scenario more similar to the first or last example above, where cooperation has an identical impact on both personal and joint outcomes. Interestingly, de Cremer and van Vugt (1999) used a step-level game in their second study and a continuous game in their third study. This article offers an opportunity to directly compare the size of the SVO effect across these game types. In the continuous game they found that prosocials contributed more than proselfs with an effect size of D = .55 (Glass, 1976). In the step-level game they again found that prosocials contributed more than proselfs, but with a smaller effect size of D = .31. There is also other evidence that suggests that SVO effects are more consistent in continuous social dilemmas than step-level social dilemmas. In coin exchange games, which are very close in structure to continuous public goods games, SVO effects have been consistently found and appear to be quite robust (de Cremer & van Lange, 2001; McClintock & Liebrand, 1988; Smeesters, Warlop, van Avermaet, Corneille, & Yzerbyt, 2003). Conversely, a series of recent studies has shown that in step-level resource dilemmas, SVO effects are found only when some form of experimental uncertainty is introduced (de Kwaadsteniet, van Dijk, Wit, & de Cremer, 2006; van Dijk, de Kwaadsteniet, & de Cremer, 2009). These studies suggest that when there is no uncertainty and all players fully understand the structure of the step-level game, groups coordinate on an equal division rule. When uncertainty is introduced, however, decisions are instead governed by individual differences, such as social motives.
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Whether the interaction is ongoing or occurs once is another important issue for the provision of public goods. Data suggest that repetition of games over multiple trials has differential effects in continuous and step-level public goods games. In continuous games, cooperation rates consistently decrease over multiple rounds (Ledyard, 1995). This pattern, although not universally reported, was shown by Isaac, Walker, and Thomas (1984) and Andreoni (1988), among others. The impact of repeated trials on contributions in step-level games is much more mixed. For example, an increase in cooperation over trials was reported by Bagnoli and McKee (1991), whereas Suleiman and Rapoport (1992) reported a decrease over trials. These mixed results may reflect the fact that if contributions on early trials fail to meet the provision point in a step-level game, they may either rise to the level of meeting the provision point or drop to no contributions at all. In addition, in a step-level game, contributions that exceed the provision will likely drop on subsequent rounds.
The Transition From Conflict to Coordination Although most examples of step-level games in the literature have one provision point, it is easy to conceive of a game with multiple steps. Indeed, if one imagines a game with many steps, it becomes barely distinguishable from a continuous game (for an example, see Marwell & Ames, 1979). Conversely, a continuous game as typically implemented becomes a multiple step-level game because contributions are represented as whole units of points or money. These relationships suggest that it is not the mere presence of provision points (or steps in the function) that shifts a game of conflict to a game with coordinated solutions. Figures 4 and 5 depict the relationship between the value of a public good and contributions for a continuous public goods game and a steplevel game, respectively. Figure 4 depicts the function for the continuous game described earlier. Zero contributions to the public good correspond to a value of zero of the public good. Starting from this origin, the function can be represented as a series of small steps: A contribution of 1 unit increases the value of the public good by 1.5 units, a contribution of 2 increases the value of the public good by 3, and so forth. Because, as implemented, the amounts of contributions are represented in discrete and not continuous units, this conceptually continuous game, in practice, consists of many small steps. If it is not the existence of steps in the function (i.e., provision points), what is it that distinguishes a public goods game that is inherently conflictual from one that presents the opportunity for a stable, coordinated solution? The distinction centers on the net return that a player expects from a unit of contribution. If, at every location in
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Figure 4. Relationship between the value of the public good and contributions for a continuous public goods game
the function, one incurs a net loss in outcome by contributing a unit, then players are always tempted to contribute less regardless of what others do. As a result, the game presents conflict between individual and collective interests. In the language of social interdependence theory, the interdependency is dominated by mutual FC and there is no BC. More formally, let the value of the public good, Vp, be a continuous increasing monotonic function, f, of the sum of the individual contributions, Yi: Vp = f (S Yi), where the summation is across r players. If an equal share of the public good is allocated to each person (i.e., each player gets Vp/r, as is the case in most experimental applications), the game presents a conflict between individual and collective interests when the rate of change in Vp is less than group size, r, for all values of S Yi. For the typical experimental game, the function is linear: Vp = cS Yi, c > 0. In this case, there is always a conflict between individual and collective interests if c < r. When c < r, there is a dilemma because the player’s share of the increment in the public good does not compensate for a unit of contribution, and one is always tempted to contribute less. If c ≥ r, there is no dilemma. If c = r, the individual is indifferent between contributing one or more units of endowment to the public pool and keeping them. If c > r, everyone fares better by contributing. Extending this logic to a step-level function, let d be the increment in value of the public good at a provision point and p be the total contributions necessary to satisfy the provision point. If d > r, then no player is tempted to reduce her or his contribution by one unit when the provision point is reached, that is, when S Yi = p. However, d > r is a necessary but not sufficient condition to ensure that a coordinated solution is stable. It is also necessary to show that a solution exists that does require any player to contribute more than d/r to reach the provision point. As depicted by the dashed line in Figure 5,
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Figure 5. Relationship between the value of the public good and contributions for a step-level game
consider a linear function starting at the origin of (0, 0) and continuing through the point (p, d). If the slope of this line, s, is greater than 1 (s = d/p > 1), then at least one solution exists that is an equilibrium if p can be equally divided among the players. That is, if s > 1 and each player contributes p/r, then each player’s compensation exceeds her or his contribution because p/r is less than d/r. Even if players’ contributions are not equal, any solution in which every player’s contribution to reaching the provision point is less than d/r is a stable solution. In this case, the provision of the public good is not necessarily a conflict between individual and collective interests; it can be framed as a coordination problem. Weber et al. (2004; also see van Dijk & Wilke, 1995, 2000) noted that people search for rules that guide decisions in interdependent relationships. In the case of step-level public goods games, a particularly compelling rule, suggested by concepts such as equity and fairness, is to share equally the cost of satisfying a provision point. A similar notion is suggested by the concept of focal points in coordination (Mehta, Starmer, & Sugden, 1994; Schelling, 1960). A focal point is a salient solution to a coordination problem. The foregoing analysis identifies another reason to favor equal divisions of contributions in satisfying a provision point. If the provision point in a step-level game permits a solution that is an equilibrium, then an equal division will certainly be an equilibrium, whereas other distributions of contributions that satisfy the provision point may not be. In the foregoing example depicted in Figure 5, each of three players contributing 5 to reach the provision point of 15 is an equilibrium: 5 is everyone’s best response to the others’ contributing 5. However, if Players A, B, and C contribute 3, 3, and 9, respectively, to reach the provision point, Player C’s best response is not 9 but 0. Thus, this latter solution is not an equilibrium. Aside from concepts of fairness and equity, equal divisions of contributions are more likely to provide stable, coordinated solutions to step-level games than unequal divisions, as long as the public good is equally distributed.
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Figure 6. Relationship between the value of the public good and contributions for a game with two steps
It is informative to note that the superimposed line in Figure 5 represents the same linear function as depicted in Figure 4. Indeed, the provision point (p, d) is a point on the continuous function in Figure 4. Thus, any solution that reaches the provision point in a game that uses this step-level function is also a solution for the continuous game that uses the continuous function depicted in Figure 4. Although such a solution may be an equilibrium in the step-level game, it is not an equilibrium in the continuous version. Thus, reframing a continuous game into a one-step game may create an equilibrium. However, adding more steps may also destroy an equilibrium. Figure 6 adds another step to the function by defining a second provision point: If total contributions are 30, the public good is valued at 45 and each of the players receives 15 as a share of the public good. If this were the only step, every player’s best response to the others’ contributing 10 would be to contribute 10 and there would be no dilemma. However, the existence of the second provision point at 15 provides an incentive for each to contribute less than 10. That is, in this two-step game, if Players B and C were to contribute 10, Player A would earn more by contributing nothing. B’s and C’s contributions would satisfy the lower provision point, creating a public good of worth 22.5, and A would get 17.5 (10 from the private account and 7.5 from the public account). Thus, in this two-step game, everyone contributing her or his total endowment is Pareto optimal but is not a Nash equilibrium. How far can one push this approach to removing the inherent conflict in a continuous public goods game? If imposing one or two steps removes the inherent conflict in the game depicted in Figure 4, do three, four, or more steps also remove it? The answer centers on determining whether equal-contribution solutions at each provision point are stable in the sense that each player’s contribution of a fair share is the best response to the others’ contributions of fair shares. In this game, r = 3 and c = 1.5. Consider imposing 10 equalsized steps. In this case, the amount of contributions, p, to go
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Abele et al. from one step to the next is 3, and the increment in the value of the public good at each step, d, is 4.5 (i.e., d = 1.5 × 3 = 4.5). Thus, each player’s fair share contribution to move from one provision point to the next is 1, and each gains 1.5 as a share of the public good (i.e., d/r = 1.5). However, by starting at the highest provision point and stepping down to the next lower, one can show that at every provision point, except the lowest one, each player is tempted to defect from the equal division solution. For example, suppose that each player contributed 4 points of her or his 10-point endowment to reach a provision point of 12. The public good would be worth 18 in this case, and each would earn 6 from the points remaining in the private account and 6 as the share of the public good—12 points. However, each of the players’ best response to the others contributing 4 would be to contribute either 1 or 0, either of which would lead to an outcome of 13.5. In repetitions of such a game, the economic pressure on each player would be to lower her or his contributions. The only point at which this pressure would be removed is when (if ever) they each contributed 1 to satisfy the lowest provision point of 3. In this case, they would each earn 10.5, which is slightly better than simply keeping their endowment of 10. Van de Kragt et al. (1983) claimed that the minimal contributing set game is a structural means of removing the inherent conflict between individual and collective interests in public goods problems. We are concluding that steplevel games, more generally, provide a way of transforming a continuous public goods game into a game that has a coordinated, stable solution. Moreover, we have identified some boundary conditions associated with the number of steps as well as their location and size. To summarize, segmenting a continuous public goods game into steps can provide the opportunity for a stable, coordinated solution to a public goods game. However, providing several steps is often counterproductive because, with the existence of lower steps, higher steps may no longer be equilibria. Nonetheless, as we address in the next section, our analysis suggests a strategy that practitioners of fund-raising often employ. Although segmenting one iteration of a continuous game into multiple steps may have limited value in promoting contributions via coordinated solutions, decomposing it temporally into a series of single-step games could be effective. For example, suppose that three players were given the opportunity to contribute 1 point in each of 10 subgames, with each subgame having a provision point of 3 yielding a public good value of 4.5. Then the stable coordinated solution to each subgame would be for each to contribute 1 point to reach the provision point. Once the three players obtained the provision point, there would be no temptation for them to defect on subsequent subgames. Thus, in this manner, temporally segmenting a continuous game into several single-step games could promote contributions to the public good.
Applied Implications Behavioral scientists are often interested in using public good problems to simulate dilemmas encountered in the social world. In this endeavor, it is useful to incorporate features of the real-world dilemma into the game. One question is whether the naturally occurring examples of public good and resource dilemmas more closely resemble continuous or step-level games. Consider the often cited example of providing public broadcasting in the United States. Public radio and public TV are public goods in the sense that no one is excluded from listening or viewing. Moreover, public broadcasting stations heavily rely on fund-raising drives to provide this public good. Although one could conceive of a provision point below which a station ceases to exist, the salient contingency is that programming will be reduced or expanded depending on the success of the fund-raising drive. The economic temptation is to free ride on the contributions of other listeners because the expected increment in the quality or quantity of programming because of one’s $25 or $100 donation is not sufficient to offset the investment for most listeners. One applied goal of experimental research on dilemmas is to learn how to reinforce behavior that is in the interest of the collective in real-life dilemmas: in environmental issues and in other cases where a public good needs to be provided or a nonexcludable resource preserved. An example of this would be the renovation of the public local library financed through donations or the maintenance of recreational areas or public day care centers. Real-world dilemmas are typically not dilemmas with an obvious or clearly defined provision point. Interestingly, however, practitioners often reframe situations so that they appear to have provision points, employing several techniques to counter the individual’s assessment that the return in public good is insufficient to justify a contribution. For example, fund-raisers for public broadcasting often add other incentives such as gifts or publicity (announcing a contributor’s name). More pertinent to our analysis, they also create artificial steps in the payoff function and frame the situation in a way that resembles a step-level game. Consider, for example, announcements such as, “We need to raise $1,000 within the next hour to support the current program” or “We need to raise $500 in the next 10 minutes to receive a matching grant of $1,000 from sponsor X.” Such announcements reframe the larger continuous public goods problem into a series of smaller step-level problems. They do so in one or both of two ways. First, they suggest the presence of a step (e.g., saving the current program). Second, they reduce the apparent size of p—the amount of contributions necessary to reach the step (e.g., “We need to get only five $100 contributions to get the matching grant”). If a public goods problem can be convincingly reframed as a series of step-level problems, the psychological dynamics can potentially shift from conflict to coordination.
398 Teamwork can also be conceptualized as a public good game (Kerr, 1983). Teamwork, which is characterized by a linear relationship between each team member’s effort and the group product, is likely to invite free riders. But those group tasks that require a specified input to achieve a group reward should be less likely to induce free riding (Arnscheid, Diehl, & Stroebe, 1997). As such, provision points can be regarded as group goals, which have been shown to increase group performance as long as they are specific (for an overview, see O’Leary-Kelly, Martocchio, & Frink, 1994).
Conclusions Experimental implementations of public goods games come in two varieties: continuous and step level. Conceptually, they represent two distinctly different types of social interdependency. Continuous public goods games pit individual against collective interests and conform to two characteristics often ascribed to social dilemmas: Each individual fares better by contributing nothing to the creation of the public good, regardless of how much others contribute, and everyone fares better if they all contribute as much as possible rather than if they all contribute nothing. In the terminology of social interdependence theory, continuous public goods games are a discordant mix of RC and mutual FC. In the terminology of game theory, everyone contributing nothing is the unique Nash equilibrium and everyone contributing as much as possible is a Pareto efficient solution.7 By contrast, a single, step-level game has several Nash equilibria: Any combination of individual contributions that minimally satisfy the provision point is a Nash equilibrium as long as no one’s contribution exceeds the individual share of the public good. Step-level games are a mix of RC and BC and can afford mutually beneficial outcomes if players coordinate their decisions. That is, single-step games can be framed as coordination problems. Because of these differences, we offer the following recommendations. First, reviews of the literature should clearly distinguish the form of the game and not generalize, either explicitly or implicitly, findings from one type of game to the other. We are not claiming that empirical findings never generalize, but in the absence of data from both types of games, there are no conceptual reasons to assume that they do. Second, terminology should not blur the distinction between the two types of the public goods games. Specifically, including both types under the category of social dilemmas blurs the distinction and is somewhat misleading when applied to single-step games. Single-step games, along with games such as BOS, are more aptly called social coordination games because they afford solutions that are mutually beneficial to all players. This designation is not meant to imply that such games never contain an element of conflict. In BOS, the wife prefers the coordinated solution of both going to the opera (O, O) whereas the husband prefers the
Personality and Social Psychology Review 14(4) coordinated solution of both going to the football game (F, F). Nonetheless, they both prefer to coordinate successfully to attain either (O, O) or (F, F) over not coordinating; thus, coordination is the dominant goal. Third, and related to the first recommendation, more research should directly contrast the two types of games. As our selective review suggests, most comparisons between the games are across studies. For example, we argued that nonbinding communication may serve different functions and affect decisions in different ways across the two types of games. However, much of the empirical evidence is indirect and rests on comparisons across studies that differ in several ways. Few studies assessed communication effects across the two types of public goods games in one experiment (exceptions are Abele et al., 2009; Bornstein, 1992). Fourth, our analysis shows that continuous and singlestep games are different in important ways but one can blur the distinction by segmenting a continuous function into steps or adding steps to a single-step game. We identified characteristics of the function that conceptually mark the transition from a dilemma to a coordination problem. However, the interesting and potentially useful questions are when the psychological shifts occur and what the behavioral implications are. For example, consider decomposing a continuous game into two steps as illustrated in Figure 6. Each provision point presents opportunities for coordinated solutions if considered separately. However, our analysis suggests that having both provision points makes a solution that satisfies the higher provision point unstable in the sense that it is not a Nash equilibrium. Compared to solutions that satisfy the lower provision point, one might expect that the solution that satisfies the higher provision point would be less likely to occur and less likely to prevail once it occurred in an iterated version of this game. However, coordinating on the higher provision point (i.e., everyone contributes all of their endowment) collectively dominates every other solution (i.e., including those that satisfy the lower provision point). In addition, allowing for the fact that players rarely fully analyze the contingencies, having multiple provision points might disrupt attempts to coordinate on any one, resulting in behavior in multiple-step games that resembles behavior in a continuous game. These are empirical issues that have not been addressed. In sum, we make a plea for a much more careful consideration of the conceptual nature of the interdependencies that are modeled in experimental games. In pursuit of good methodology, the choice of experimental games should be carefully scrutinized in light of the experimental objectives. If, for example, the intent is to study conflict resolution, a continuousform public goods game is more appropriate than a step-level game. This exercise is not a means to an end but should be understood as a way to ensure cleanly designed experiments and validly measured dependent variables. Thus, any research reporting a study that uses an experimental game should
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Abele et al. include a justification for the form of the game, and reviews of the literature should avoid generalizing results from one form of a game to a superficially similar game when the underlying interdependencies are different. Walter Mischel (1968) contended 40 years ago that behavior is a function of the person and the situation. On one hand, the person by situation framework has been used extensively to study how different personalities react to situation. On the other hand, the formulation underscores the importance of context in understanding social behavior. Social scientists interested in conflict, cooperation, and coordination should use the conceptual tools provided by social interdependence theory and game theory for classifying the social context in which behavior is embedded (Abele, in press; Kelley et al., 2003). By neglecting or ignoring a comprehensive representation of the interdependencies in the social situation, we risk sacrificing our understanding of why people behave differently in situations that superficially appear to be similar. Declaration of Conflicting Interests The author(s) declared no potential conflicts of interests with respect to the authorship and/or publication of this article.
Financial Disclosure/Funding The author(s) received the following financial support for the research and/or authorship of this article: Preparation of this article was partially supported by National Science Foundation Grant BCS 0744696 to the first author and by National Science Foundation Grant SES 0603858 to the second author.
Notes 1. In a resource dilemma, a common resource pool exists for consumption for a group. Resource units that have been harvested by one group member are not available to another. Moreover, resource dilemmas are often played over repeated trials, and the resource is replenished at a rate that is proportional to the remaining resource after each trial. It is also usually the case that the resource can be exhausted, leaving nothing for the players to harvest and no opportunity for the resource to replenish. Hence, a modest consumption could be viewed as the “cooperative move” but is not always in the best interest for the group, depending on the level of the resource and the replenishment rate. Consequently, the conclusions in this article are conceptually and methodologically more pertinent to public goods games than resource dilemma games. For a more detailed analysis of resource dilemma games see, for example, Budescu, Rapoport, and Suleiman (1995). 2. Bornstein (1992) proposed a game that models intergroup conflict over continuous public goods and a game that models intergroup conflict over step-level public goods (Rapoport & Bornstein, 1987). He compared the effects of between- and within-group communication in these two different team games, which are more complex than the simple games.
3. To be technically correct, what we call Nash equilibrium is really a Nash equilibrium in pure strategies. 4. Similarly, Ledyard (1995) made the argument that the step-level public goods game is more like the chicken game (another version of a coordination game) than the prisoner’s dilemma. 5. The step-level resource dilemma can legitimately be viewed as a take-some variant of the give-some step-level public good game. 6. Note that the predictions were made for prosocials seeking to maximize collective gains. For prosocials seeking to maximize equality, the predictions would be identical in the first example but reversed for the latter two. 7. See Note 3.
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Bios Susanne Abele is a Research Scholar and Research Assistant Professor at Miami University. Previously, she held positions at the Rotterdam School of Management at Erasmus University Rotterdam (Netherlands), the University of Mannheim (Germany), and a behavioral finance consultancy in Frankfurt (Germany). Her work has appeared in Journal of Personality and Social Psychology, Journal of Experimental Psychology and Organizational Behavior and Human Decision Processes. Professional memberships include Society of Experimental Social Psychology (Fellow), the European Association of Social Psychology (Member), and the Society for Judgment and Decision Making (Member). Her research interests are coordination in social behavior, behavior in public good games, social information processing in interdependent decision making, and group performance and collective choice. Garold Stasser is Professor of Psychology at Miami University. His published work has appeared in Psychological Review, Review of Personality and Social Psychology, Psychological Inquiry, Journal of Personality and Social Psychology, Journal of Experimental Social Psychology and Organizational Behavior and Human Decision Processes. He has served as an associate editor for Personality and Social Psychology Bulletin and Journal of Experimental Social Psychology. Professional memberships include Association for Psychological Science (charter member and Fellow), Society of Experimental Social Psychology (Fellow), and the European Association of Social Psychology (Affiliate). His research interests are communication in decision making groups, coordination of social behavior, collective choice and problem solving and computational models of social interaction. Christopher Chartier is a graduate student in Psychology at Miami University. His research interests include behavior in social dilemmas and the effects of people’s social value orientation, more specifically what motivations and preferences account for the prosocial orientation.
