The heart of this paper is a model of social interaction in which players use costumes ... advertising campaigns are necessarily massive, and that the targeted ...
Image Advertising B. Curtis Eaton William D. White
University of Calgary Yale University Abstract
The heart of this paper is a model of social interaction in which players use costumes and other visible consumption goods as signals about the identity of other players. If these signals are informative enough, players use them to condition their social interaction. Importantly, accurate signals are mutually beneficial. This game is then wrapped in another in which players choose their costumes. There are many equilibria in this expanded game, some of which allow individuals to perfectly signal their type in all social interactions, and others of which do not. The perfect signaling equilibria Pareto dominate the others, but since there are many of them, the players face a difficult coordination problem. In this paper we explore the hypothesis that image advertising solves this coordination problem. Two implications of our theory are that image advertising campaigns are necessarily massive, and that the targeted audience for the advertising campaign is necessarily larger than the targeted group of buyers of the advertised product. We offer anecdotal evidence in support of both implications.
1
1. Introduction
For the most part, the economist's vision of the individual is founded on the notion of private consumption goods. For example, if asked to think about two women sitting down to have lunch together, most economists would think of the relationship between each woman and her food as a purely private one; in the economist’s eye, what one woman has for lunch has no bearing on the other's well being. Garlic aside, this is a sensible working hypothesis for many sorts of consumer choices.
There is, however, another sort of choice for which the fiction of private consumption goods is definitely not sensible. For example, when one of those curious fellows from the City of London puts on his bowler hat and grabs his black umbrella, he is at least as concerned about the image he is projecting to other people (i.e. what they make of him) as he is about keeping his head warm and dry. Similarly, when you look at yourself in the mirror-- when buying a new suit or getting dressed for a job interview, for example-- your behavior reflects more a concern for the image you project than a purely private relationship between you and your clothes. Engagement and wedding rings provide more obvious examples of goods that are worn primarily for the image they project.
It is decisions about these sorts of goods, which we call costumes, that are the focus of this paper. We are concerned with the kinds of decisions that Harry Rosen, haberdasher for Toronto's male power elite, will advise you about in his recent booklet – Image: The Art of Dressing Well. To quote the journalist Stephen Brunt, quoting Rosen: "The passage that all but leaps off the page is about what it means to be inappropriately attired. 'It's a no-possible-win situation that says you're either cheap, poor, without manners, illiterate, forgetful or uninvited. Any one of these could be enough to impede your march to the corner suite." (The Globe and Mail, September 6, 1990, p. 18).
We propose to take these sometimes amusing, but nevertheless interesting and perhaps important, decisions seriously. Our goal is to develop an economic theory of "image building." Our starting point is the observation that in a wide range of situations, from social gatherings to
2
job interviews, the outcomes of personal interactions depend heavily on the appropriate matching of hard to observe individual characteristics. The novel twist is to apply signaling notions to explore how "images" projected by choices of "costumes" may help to solve these matching problems.
Several generic problems exist with any type of signaling (cf Spence 1974, Frank 1988). One problem is that establishing a signaling equilibrium may involve complex coordination problems of its own. There is thus an issue of derivation; the process by which signals originate demands investigation. One central thrust of this paper is the argument that image advertising serves to solve this coordination problem.
A second problem is that hand in hand with mutually beneficial signaling can come opportunities for dissembling (i.e. fraud) which can lead a signaling equilibrium to unravel. In this paper we assume an environment in which there is no motive for fraud. Thus, while we recognize that issues of fraud are important in many circumstances (see for example Carr and Landa (1983)), these circumstances do not arise in our model.
An implication of our analysis is that when costumes serve as signals, consumers' choices of costumes are interdependent. The idea that consumption choices are sometimes interdependent is familiar. However, interdependence has typically been considered in a context of directly interdependent utility functions -- the consumption bundle of one consumer enters the utility function of another, for example. The cases of altruism and conformity are examples (cf Wintrobe 1983, Jones 1984). In the absence of directly interdependent utility functions, standard models of consumer choice and advertising assume that behavior is purely private. Consider for instance standard paradigms of advertising. At least three functions are identified: to directly inform consumers about product attributes (cf Nelson 1974); to serve an indirect informational function, where, for example, by investing in advertising, a firm may convey commitment to a product (cf Kilfflstrom and Riordan 1984 and Klein and Leffler 1981); to enhance product attributes through a process of "affect," for example serving to create pleasurable associations with the consumption of a product (ef Cafferata and Tybout 1989).
3
In all of these cases, the contribution of advertising is private. Failure to reach a potential customer may lose a sale. But it has no impact on sales to others. In our analysis, utility functions are independent, but individuals interact in social situations. Information as to type is valuable in these social interactions, hence individuals attempt to signal their type by their choices of costumes. This, of course, generates interdependent demands for the costumes that are used as signals. We show that through image advertising firms often can and will engineer a signaling equilibrium. Interestingly, an image advertising campaign that does not reach most of the consumers in the relevant market will fail to create an accepted image, and hence will have minimal impact on demand for the advertised good.
In Section II we outline a two-stage game of social interaction: in stage 1, each player chooses a costume; subsequently, in stage 2, players meet in random, pairwise encounters in which they use costumes as clues about the underlying characteristics of other players. We close this section with a discussion of the nasty coordination problem that bedevils this game. In Section III we show how image advertising can solve this coordination problem. In Section IV we close with a brief discussion of some of the stylized facts of image advertising in the context of our theory.
In common usage, the terms "image" and "image advertising" are slippery concepts, more easily illustrated than defined. In contrast, in our model they are perfectly well defined. Giving these slippery concepts precise meaning is, we believe, one contribution of this paper.
II. The Game of Dress-Up
In this section we explore a two stage game in which players choose costumes in the first stage, and engage in a series of random, pairwise, anonymous encounters in the second stage. Naturally, the costumes bought in the first stage may serve as type signals in the encounters that occur in the second stage. We begin by describing the encounter game. Then we find equilibrium actions for a typical encounter, taking the known frequency distribution of player types over costumes as given.
4
Building on these results, we step back to the first stage in which players choose costumes to find the equilibria of the entire two stage game. There are three distinct sorts of equilibrium, and many equilibria of each sort -- hence a difficult coordination problem. The heart of our paper is Section III, where we examine the possibility that image advertising is successful because it helps to solve this coordination problem.
II.1 Payoffs for an Encounter
For lack of a better term we call the players in an encounter partners. Since encounters are anonymous and arise through random matches of two players, in an encounter a player's partner may be any of T possible types. For a player of type i whose partner is a player of type j, there is a unique best action which we call the appropriate action and which we denote by Aij . For reasons that will become clear, we say that action Aij is inappropriate if the partner's type is k ≠ j. The set Ai = { A1i , A2i ,….. ATi } is called the set of type specific actions for a player of type i. In addition to these type specific actions, there is a neutral action which we denote by Ni. The neutral action can be thought of as spending resources to directly determine the partner’s type as opposed to attempting to infer her type from the costume she wears. In any encounter, the set of actions open to a player of type i is then { A1i , A2i ,…. ATi , Ni}. Now consider an encounter between players of types i and j, and let ai and aj denote the player's respective actions. Player i's payoff is
(1)
Π i (ai,aj) = x ij + v + w,
where
v = y if ai is appropriate
(ai = A ij ),
v = z if ai is neutral
(ai = Ni),
5
v = 0 if ai is inappropriate
(ai = Aki ,k ≠ j ),
w = g if aj is appropriate
(aj = A ij ),
w = h if aj is neutral
(aj = Nj),
w = 0 if aj is inappropriate
(aj = A jk , k ≠ i).
The first element of player i's payoff, x ij, can be thought of as the baseline payoff for a player of type i in an encounter with a player of type j. The second and third elements, v and w, capture the type communication aspects of the game that are the focus of this paper. Notice that player i's action determines v, while player j’s action determines w. We assume that y>z>0 and that g>h>0. Then, as regards both her own action and the action of her partner, player i prefers an appropriate action to a neutral action, and a neutral action to an inappropriate action.
In Table 1 we illustrate the row player's payoff in an encounter in which the row player is type 2, the column player is type 3, and T = 3. The baseline payoff x23 has no behavioral significance since this payoff occurs in each cell of the payoff matrix. In other words, the communication aspects of the game determine payoffs that are incremental to x23 . Notice that for each player there are just three payoff relevant actions since any action is either appropriate, inappropriate, or neutral. The largest possible payoff occurs when both players choose the action that is appropriate, given their partner's type. And the lowest possible payoff occurs when both players choose an action that is inappropriate, given their partner's type. If both players choose neutral actions, they are both better off than if they both choose inappropriate actions (since z + h > 0), but they are worse off than if they choose appropriate actions (since z + h < y + g).
6
Table 1
Row Player’s Payoffs Row Player:
Type 2
Column Player: Type 3
a3 = A13
a3 = A23
a3 = A33
a3 = N3
Inappropriate
Appropriate
Inappropriate
Neutral
a2 = A12
x23
x23
x23
x23
Inappropriate
+0+0
+0+g
+0+0
+0+h
a2 = A22
x23
x23
x23
x23
Inappropriate
+0+0
+0+g
+0+0
+0+h
a2 = A32
x23
x23
x23
x23
Appropriate
+y+0
+y+g
+y+0
+y+h
a2 = N2
x23
x23
x23
x23
Neutral
+z+0
+z+g
+z+0
+z+h
It is useful to represent the payoff structure for an encounter more compactly by focusing on payoff relevant actions, and by suppressing the baseline payoff. Table 2 gives the row player's payoff in terms of the three payoff relevant actions for an encounter in which the player types are arbitrary. In each cell, the first payoff element is determined by the row player's action and the second by the column player's action. Table 2
Row Player’s Payoffs in Terms of Payoff Relevant Actions Appropriate
Neutral
Inappropriate
Appropriate
y+g
y+h
y+0
Neutral
z+g
z+h
z+0
Inappropriate
0+g
0+h
0+0
7
II.2 Equilibrium Strategies for an Encounter
In an encounter both players observe their partner's costume before they choose an action, so it is possible for a player to use the partner's costume as a type signal. We want to know when a player will regard the partner's costume as a type signal. More precisely, we want to know when a player of type i will choose an action from the set Ai of type specific actions in preference to the neutral action Ni.
Define P(t,c) as the relative frequency (or proportion) of players wearing costume c who are type t, and suppose that all players know this frequency distribution. In choosing an action the player faces the following dilemma. Since encounters are anonymous, the partner's type is not directly observable. But the frequency distribution of costumes over types permits the player to form subjective probabilities regarding the partner's type. If the player chooses an action from the set of type specific actions, the action may be appropriate or it may be inappropriate. Then, since the player prefers to take an appropriate action as opposed to a neutral action, and a neutral action as opposed to an inappropriate action, the player will choose a type specific action only if the subjective probability that the chosen type specific action is appropriate is sufficiently high. Let Ω (c) denote the most frequent player type wearing costume c, and Φ (c) the relative frequency of player type Φ (c). Clearly,
(2)
Φ (c) = P(Ω (c), c).
Then, if player i's partner is wearing costume c, the best action from the set Ai of type specific actions is AΩi ( c ) . This action will be appropriate with probability Φ (c) and it will be inappropriate with probability 1- Φ (c). (Throughout the paper we assume, strictly for convenience, that players are are atomless. The numbers of players of each type are then to be interpreted as real numbers, not as integers.) The other viable strategy for player i is to take action Ni. The expected payoff to action AΩi ( c ) is no smaller than the expected payoff to action Ni if
8
Φ (c )[ y + u ] + [1 − Φ (c )][ 0 + u] ≥ [ z + u ]
u ∈{g , h,0} .
Whether u is equal to g, h, or 0 is determined by the partner's action: it is g if the partner's action is appropriate, h if it is neutral, and 0 if it is inappropriate. The inequality reduces to
(3)
Φ ( c) ≥ z / y .
Hence, in any encounter, player i has a dominant strategy: (i) take action AΩi (c ) if Φ ( c) ≥ z / y ; (ii) otherwise take action Ni.
Recall that both y and z are positive, and that y (the incremental payoff to player i if player i chooses the appropriate type specific action) exceeds z (the incremental payoff to player i if player i chooses the neutral action). Hence, 0 < z/y < 1.
The dominant strategy result is intuitive. Given that the partner wears costume c, if the subjective probability that the partner is of type Ω (c) is large enough, the player will choose action AΩi (c ) , but if the subjective probability is too small, the player will choose the neutral action Ni.
II.3 The Coordination Problem
The fundamental coordination problem in dress-up arises from the fact that all players are better off if, in stage 1, they manage to coordinate their choices of costumes in such a way that each costume is worn only by players of the same type. When they achieve this sort of coordination -perfect coordination -- costumes serve as perfect type signals, and all players get the maximum possible payoff in all encounters. The trouble is that there are as many ways of achieving perfect coordination as there are ways of assigning player types to costumes, and no director of costuming to prescribe a solution.
9
To be more precise, it is useful to look at the subgame perfect equilibria of the game in which players simultaneously choose their costumes in stage 1, and then engage is random pairwise encounters in stage 2, knowing the frequency distribution of costumes over types that is generated in stage 1. We assume that there are at least as many costumes as player types.
Corresponding to each possible frequency distribution generated in stage 1, there is a stage 2 subgame. From above we know the equilibrium strategies for these subgames. Then, to identify the subgame perfect equilibria of the entire two stage game, we need to identify the frequency distributions such that no player regrets her choice of costume in stage 1, given that players implement the associated equilibrium strategies in all stage 2 subgames.
At the one extreme are all the equilibria in which all players perfectly signal their type. Suppose in stage 1 that player choices of costumes are such that Φ (c) = 1 for all costumes c that are purchased. Then in all stage 2 encounters, both players know with certainty the type of the other player, and choose the appropriate action for their partner's type. Since this generates the highest possible payoff in all encounters for all players, no player regrets her choice of costume in stage 1. There are, obviously, many perfect signaling equilibria.
In a perfect signaling equilibrium the costumes have a signaling value, in addition to any inherent use value (assumed to be identical for all costumes) they might have. Consider a player of type i. Relative to a costume for which Ω (c ) ≠ i , any costume for which Ω (c) = i gives the player a payoff in each encounter that is larger by amount g, since the former costume elicits an inappropriate action in all encounters while the later elicits an appropriate action. Notice too that player i does not capture all the gains that arise when she chooses a costume for which Ω (c) = i in preference to one for which Ω (c ) ≠ i , since all the partners she encounters in stage 2 are better off by y.
At the other extreme are all the equilibria that involve no (effective) type signaling. Suppose in stage 1 that Φ (c) < z/y for all costumes. Then, in all stage 2 encounters both players will choose a neutral action. Further, although each player would have preferred in stage 1 to have chosen a
10
costume that did serve as an accurate type signal, given the choices made by other players in stage 1, there are no such costumes. Hence, no player regrets her choice of costume in stage 1. There are, obviously, many non-signaling equilibria. In all these equilibria, all costumes are equally attractive to all players.
Clearly, mixed equilibria in which some players manage to signal their type and others do not are also possible. Suppose that player choices of costumes in stage 1 are such that, for some costumes, Φ (c) = 1, and for others, Φ (c) < z/y. Then players who chose the first sort of costume will be sending perfect signals regarding their type, and those who chose the second sort will be sending no effective signal. For this situation to constitute an equilibrium we must suppose, in addition, that players who could have chosen a costume in stage 1 that would have perfectly signaled their type in stage 2, did buy such a costume.
Holding the configuration of stage 2 encounters fixed, any of the perfect signaling equilibria Pareto-dominates any of mixed equilibria, and any of the mixed equilibria Pareto-dominates any of the non-signaling equilibria.
In the game as specified, the coordination problem is overwhelming. Except by chance, the players will not arrive at any equilibrium, let alone a perfect signaling equilibrium. In the next section we see how image advertising might achieve imperfect coordination in a suitably expanded game. In a closely related paper, Arifovic and Eaton (1998) use the genetic algorithm in a framework in which dress-up is played repeatedly to explore the possibility that learning may lead to a perfect signaling equilibrium.
III. Image Advertising
In that it involves both senders and receivers, image building is like any other form of communication. And like other forms of communication, successful image building entails the solution to a coordination problem since the accurate projection of images requires both senders and receivers to have a common vocabulary of images. It is this need to establish a common vocabulary that distinguishes image advertising from other forms of advertising.
11
Fundamentally, an image advertising campaign attempts to associate an image with a product, to write a new entry in the dictionary of images. "People who display product A are projecting image I." More succinctly, "Product A is associated with image I." Like any other advertising campaign, the image campaign must communicate with potential buyers of the image product. That is, the image campaign must communicate the intended product/image association to targeted buyers – a group of people who want to project image I and will therefore buy product A, if they can be convinced that this association is accepted by their targeted audience. But this means that the image campaign must also convince the targeted buyers that the targeted audience has also received and accepted the intended association. At a minimum, this would seem to require that the image advertising campaign actually communicate the intended product/image association to the targeted audience. That is, unlike other advertising campaigns, to be effective the image campaign must communicate with a group that is broader than group of targeted buyers. As we see it, the need to communicate with both potential buyers and with the audience with whom these buyers want to communicate – the need to establish a common vocabulary of images – is what distinguishes image advertising from other forms of advertising.
This feature of imaging advertising has two immediate implications. First, image advertising will be broadly pitched, to a group that includes both targeted buyers and their targeted audience. Second, given that a successful campaign must convince the targeted buyers that a substantial portion of the targeted audience has also received and accepted the intended product/image association, to be successful an image advertising campaign must also be massive. In other words, quantity demanded is a non-concave function of expenditure on image advertising. To be more precise, and to explore related aspects of image advertising, we extend the game of dressup to include image advertising. It should be clear, however, that these two features of images advertising are quite general.
12
III.1 The Image Advertising Model
We need a little more notation. Let ni (i = 1, T) denote the number of players of type i, n ( = ∑ n i ) the total number of players, pi (=ni/n) the proportion of all players who are type i, and M the total number of products. We assume that all players know ni (i = 1,T) and M. Since players are atomless, we can interpret ni and n as real numbers. In contrast, M is an integer. In the context of dress-up, the images to be associated with costumes are player types. We will think of the advertiser as trying to create the association of costume c and player type i by broadcasting the following message: "All players of type i who receive this message will buy costume c, and all players of types other than i who receive this message will not buy costume c."
Targeted buyers are the ni players of type i, and the their targeted audience is the entire group of n players, since players of type i interact with the whole population.
The technology of advertising is captured by the following function: (4)
Λic = f ( E ci ) .
where Eci is amount spent to communicate the message and Λic is the proportion of the entire population of players that receives the message. We assume that f (0) = 0, and that f ( E ic ) is increasing in its argument for all Eci such that Λic < 1.
We assume also that the technology of message sending is such that anyone who receives the message can infer Λic . This important assumption is not entirely unrealistic. Anyone who receives a message broadcast in conjunction with a telecast of the Super Bowl, for example, can be sure that something like 150 million other viewers also got the message. Similarly, elaborate and expensively produced TV ads assure the viewer that the advertiser intends to reach a large audience -- the more elaborate and expensive the ad, the larger the intended audience. It is also possible for an individual to make inferences regarding the coverage of a campaign from the number of times the individual is exposed to a particular ad, or series of ads. What is crucial for
13
our story is that people who receive image messages are able to make inferences regarding the number of other people who also received the message. It is, we believe, realistic to suppose that people can and do make such inferences. To facilitate analysis, we assume that these inferences are perfectly accurate, which is, of course, quite unrealistic.
It is convenient to assume that pi is large relative to 1/M for all player types. Image advertising is definitely not attractive in our model unless this restriction is satisfied for at least one player type -- to see this, notice that any costume that managed to establish a universally accepted image of type i is trading a market share of 1/M for a market share of pi. As a matter of convenience, we will assume that the restriction is satisfied for all player types. Specifically, we assume that pi > 1/(M – 1).
For simplicity we want to assure that in their stage 2 encounters players respond to costumes that have not been advertised with a neutral action. A sufficient condition is that none of the relative player frequencies in the group of players for which there has been no attempt to establish an image costume be greater than z/y. This will be true if the number of advertised costumes is small and if, for all player types i, pi is small enough relative to z/y. Since we want to focus on image advertising, we suppose that the prices of all costumes are identical (and larger than marginal cost of producing a costume). In addition, we assume that each player will buy one costume for reasons that are unrelated to dress-up. A costume then has an inherent value to a player, and possibly a value as a type signal. The value as a type signal can be positive or negative, depending on whether the image associated with the costume is the player's own type or some other type. For each player, one costume, which we call the inherently preferred costume, has an inherent value that is marginally larger than the inherent value of all other costumes. The inherently preferred costumes of all player types are uniformly distributed over the M costumes. However, the margin of preference for the inherently preferred costume is so small that a player will always choose an inherently non-preferred costume that serves as an accurate type signal to an inherently preferred costume that does not, and will choose an inherently non-preferred costume that does not serve as a type signal to an inherently preferred costume that serves as an inaccurate type signal.
14
III.2 One Image Advertising Campaign
Now let us look at the case in which there is just one image campaign. Specifically, suppose that, just before players buy their costumes in stage 1 of dress-up, the firm that produces costume c spends E ic to create an association of costume c with player type i.
The players who do not receive the advertiser's message are easy to model. Since they have no way of coordinating their actions, they will buy their inherently preferred costumes, their purchases will be uniformly distributed over the M available costumes, and they will choose the neutral action in all stage 2 encounters.
As regards the players who receive the advertiser's message, some additional terminology is useful. We will call these players messaged players, and we will speak of the messaged players as accepting or rejecting the advertiser's intended image in stage 1 of dress-up, and of validating or failing to validate the intended image in their stage 2 encounters. When we say that the messaged players accept the advertiser's intended image in stage 1, we mean that messaged players of type i buy costume c, that messaged players of types other than i whose inherently preferred costume is c randomly choose among costumes other than c, and that all other messaged players buy their inherently preferred costume. And when we say that the messaged players reject the advertiser's intended image in stage 1, we mean that they buy their inherently preferred costumes. When we say that the messaged players validate the intended image in their stage 2 encounters, we mean that if their partner in any encounter is wearing costume c they choose the type specific action that is appropriate for a partner of type i, and when their partner is wearing a costume other than c they respond with a neutral action. And when we say that the messaged players fail to validate the intended image in stage 2 encounters, we mean that they choose the neutral action in all encounters regardless of the costume worn by their partner.
We want to answer two closely related questions. In stage 1 of dress-up, will the messaged players accept the intended image? In stage 2 encounters, will the messaged players validate the intended image?
15
Notice first that, in stage 1, a messaged player will accept the intended image if it is anticipated that in stage 2 encounters messaged players will validate the image. To see this, suppose messaged players do anticipate validation. Then, by accepting the image in stage 1, a messaged player of type i elicits an appropriate (as opposed to a neutral) action in all encounters with other messaged players, and messaged players of types other than i elicit a neutral (as opposed to an inappropriate) action in their encounters with other messaged players.
So, to answer these two questions, we will suppose that the image is accepted in stage 1, and ask whether it will be validated in stage 2 encounters. Using the dominant strategy result from Section II.2, we know that a messaged player's decision to validate the advertiser's intended image depends on the subjective probability that a player wearing costume c is of type i. Only if the subjective probability is large enough (≥ z/y) will the messaged player respond to costume c with a type specific action appropriate for a player of type i. Given the assumptions we have made, we can calculate that probability. That is, supposing that the intended image is accepted in stage 1, we can determine the circumstances in which it will be validated in stage 2.
A messaged player who makes the provisional assumption that the intended image is accepted in stage 1 will reason as follows. Unmessaged players will choose their inherently preferred costumes in stage 1, and their choices will be uniformly distributed over the M available costumes. This is true even if they are sophisticated enough to infer that some firm has an incentive to try to establish an image for its costume. The expected number of unmessaged players is (1 - Λic )n. (It is here that we use the assumption that a messaged player can infer Λic ). The expected number of unmessaged players who buy costume c is (1- Λic )n/M, and the expected number of unmessaged players of type i who buy costume c is (1 - Λic )ni/M. The expected number of messaged players is Λic n, and given the provisional assumption that the image is accepted by these players, the expected number of players from this group who buy costume c is Λic ni, and all of these players are type i. Hence, in the group of players wearing costume c, the expected relative frequency of type i players, Φ ic , is
16
(5)
(1 − Λic ) ni / M + Λic n i Φ = (1 − Λic ) n / M + Λic ni i c
Naturally, when Λic = 0, Φ ic = ni/n = pi, and when Λic = 1, Φ ic = 1. Notice also that Φ ic is an increasing function of Λic . Let Λ be the value of Λic such that Φ ic = z/y, and implicitly define E by Λ = f( E ). By assumption pi < z/y, so Λ > 0 and E > 0. Hence, Φ ic ≥ z/y only if Λic ≥ Λ > 0 (or Eci ≥ E >0). So, if Λic < Λ (or Eci < E ), then Φ ic < z/y, and messaged players will not c validate the intended image in stage 2 encounters, even if the image is accepted by messaged players in stage 1. But there is then no reason for messaged players to accept the image in stage 1. We conclude that messaged players will reject the advertiser's intended image in stage 1 if Λic < Λ (or Eci < E ). In other words, there is threshold level for image advertising below which it has no effect on anyone's choice of costume. Conversely, if Λic ≥ Λ , then Φ ic ≥ z/y, and messaged players will validate the intended image in stage 2 encounters, assuming that the image is accepted in stage 1. In this case there is good reason for messaged players to accept the intended image in stage 1: by accepting the image, messaged players of type i elicit an appropriate (as opposed to a neutral) response in their encounters with other messaged players and messaged players of types other than i elicit a neutral (as opposed to an inappropriate) action in their encounters with other messaged players. We conclude that messaged players will accept the advertiser's intended image if Λic ≥ Λ .
It is useful to express these results in terms of the self-confirming beliefs of messaged players that are implicit in what we have said. We will look first at the case in which image advertising is effective ( Λic ≥ Λ ). We propose the following self-confirming beliefs.
17
(B.1): When Λic ≥ Λ , all messaged players believe (i) that all other messaged players will accept the advertiser's intended image in stage 1 and (ii) that all other messaged players will validate the intended image in their stage 2 encounters.
Beliefs (B.1) lead the individual messaged player to adopt the following strategy: accept the proposed image in stage 1, and validate it in stage 2. In other words, these beliefs are selfconfirming. It may be useful to articulate this crucial point more carefully. Given beliefs (B.1), the individual messaged player believes that all other messaged players of type i will buy costume c and that all other messaged players of types other than i will buy a costume other than c. These beliefs lead to a subjective probability Φ ic ≥ z/y since Λic ≥ Λ . Hence these beliefs lead the individual messaged player to validate the intended image in stage 2 encounters -- that is, to respond to costume c with an action appropriate for a player of type i and to other costumes with a neutral action -- thus confirming part (ii) of (B.1).
Now consider the decision to buy a costume in stage 1. Consider first a messaged player of type i. She will anticipate an appropriate response in all encounters with other messaged players if she buys costume c and a neutral response if she buys any other costume. Since an appropriate response is preferred to a neutral, and since the choice of costume has no effect on the actions of unmessaged partners, beliefs (B.1) lead a messaged player of type i to buy costume c. Now consider a messaged player of type other than i. She will anticipate an inappropriate response in all encounters with other messaged players if she buys costume c and a neutral response if she buys any other costume. Since a neutral response is preferred to an inappropriate response, and since the choice of costume has no effect on the actions of unmessaged partners, beliefs (B.1) lead a messaged player of type other than i to buy a costume other than c. Thus part (i) of (B.1) is also confirmed. The following beliefs are also self-confirming when Λic ≥ Λ .
18
(B.1)': When Λic ≥ Λ , all messaged players believe (i) that other messaged players will reject the advertiser's intended image in stage 1 and (ii) that all other messaged players will fail to validate the intended image in their stage 2 encounters.
Clearly, all messaged players are worse off in the equilibrium associated with (B.1)' than they are in the equilibrium associated with (B.1). Hence, beliefs (B.1) would seem to be salient. Now let us look at the case in which Λic < Λ . We propose the following self-confirming beliefs. (B.2): When Λic < Λ , all messaged players believe (i) that other messaged players will reject the advertiser's intended image in stage 1 and (ii) that all other messaged players will fail to validate the intended image in their stage 2 encounters.
We leave it to the reader to show that these beliefs are self-confirming. Given beliefs (B.2), image advertising is completely ineffective.
Given our proposed beliefs, (B.1) and (B.2), quantity demanded of costume c, Qc ( Eci ) , is
(6)
Qc ( Eci ) = n/M
if Eci < E
f ( Eci ) ni + [1 − f ( Eci )][ n / M ] if Eci ≥ E
Two features of this demand function are noteworthy. First is the non-concavity in quantity demanded as a function of expenditure on image advertising at Eci = E . When Eci = E , f ( Eci ) ni + [1 − f ( Eci )][ n / M ] > n/M when pi > 1/M. Of course, if pi < 1/M, image advertising is pointless since, if effective, it leads to a decrease in demand. It is for this reason that we assumed above that pi > 1/M. Second, the larger is pi, relative to 1/M, the more attractive is image advertising since the probability that the firm sells its costume to an unmessaged player is 1/M
19
and (given that Eci ≥ E ) the probability it sells to a messaged player is pi. Hence, other things equal, if there is to be just one image costume, the image will be the most frequent player type.
III.3 The Same Image for Two Costumes
Now let’s look at the possibility that two costumes establish the same image. We suppose that the firms producing costumes c and d have spent amounts Eci and Edi to establish an association between their product and player type i. The probability that any player receives message d (respectively c) is then Λid = f ( Edi ) (respectively Λic = f ( Eci ) ). We want to partition the ( Λic , Λid ) space into four regions: messaged players accept both images; messaged players accept neither image; messaged players accept image c but not image d, messaged players accept image d but not image c. As above, an image will be accepted by messaged players only if they anticipate that the images will be validated in subsequent encounters.
First we must be more specific as regards the technology of advertising. We assume that the technology is perfectly ordered. A technology is perfectly ordered if the following conditions are satisfied: (i) when Eci = Edi , both messages are received by the same group of players; (ii) when Eci < Edi , all players who receive message c also receive message d. To get some feeling for the circumstances in which the assumption would be true, suppose that television is the medium for image messages, and that different players watch different numbers of programs. The advertising technology will be perfectly ordered if the rank orderings of the available programs for all players are identical. In this circumstance, if player u watches more programs than player v, player u will receive all the messages received by player v.
The other salient assumption is that the technology of advertising is random and independent. A technology is random and independent if the probability that any player receives any message is dependent only on the amount spent to communicate the message, E. (The probability itself is f(E)). Assume again that television is the image medium, and that different players watch different numbers of television programs. If, from the set of available programs, all players 20
randomly choose without replacement the programs they watch, the technology will be random and independent. It is not at all clear which of these extreme assumptions regarding the technology of messages is more realistic. We choose to work with a perfectly ordered technology because it is more tractable. Figure 1 illustrates the proposed partition of the ( Λic , Λid ) space. Λ and Λ′ are implicitly defined by the following equations:
(7.1)
(1 − Λ ) N i / M + ΛN i z = (1 − Λ ) N / M + ΛN i y
(7.2)
(1 − Λ ′) N i / M + Λ ′( N i / 2) z = (1 − Λ ′) N / M + Λ ′( N i / 2) y
From equation (5) we see that Λ is the smallest value of Λic such that the image for costume c would be validated, if messaged players accepted the image for costume c and rejected the image for costume d. Alternatively, Λ is the smallest value of Λid , such that the image for costume d would be validated, if messaged players accepted the image for costume d and rejected the image for costume c. If both Λic and Λid are less than Λ , following results established in Section III.1, it is natural to propose that neither image will be accepted. The supporting, self confusing, beliefs are: (B.3): When Λic < Λ and Λid < Λ , all messaged players believe (i) that all other messaged players will reject the image messages they receive in stage 1 and (ii) that all other messaged players will fail to validate the intended images in their stage 2 encounters.
21
If Λic > max( Λ , Λid ), we propose that the intended image for costume c will be accepted and the intended image for costume d rejected. Given a perfectly ordered technology, all messaged players will receive message c. Further, since the technology is known to be perfectly ordered, messaged players can infer that the image message for costume c has deeper market penetration than the image message for any other good, regardless of whether they receive the other message or not. Hence, all messaged players of type i will buy costume c in preference to costume d, knowing this, all messaged players will accept the intended image for costume c and reject the intended image for costume d. The supposing beliefs are: (B.4): When Λic > max( Λ , Λid ), all messaged players believe (i) that all other messaged players will accept the intended image for costume c and reject the intended image for costume d (if they also receive this message) in stage 1 and (ii) that all other messaged players will validate the intended image for costume c in their stage 2 encounters and will fail to validate the intended image for costume d.
22
The case in the upper/left portion of Figure 1, in which Λid > max( Λ , Λic ), is, of course, symmetric, so we propose that in this portion of the figure the image for costume d will be accepted and the image for costume c rejected. Λ′ , implicitly defined by equation (7.2), is the smallest common value of Λic = Λid such that if messaged players of type i chose costume c or costume d with probability 1/2, and other messaged players bought neither costume, the intended images of both costumes would be validated in subsequent encounters. Clearly, Λ ′ > Λ . When Λic = Λid ≥ Λ′ we propose that both images will be accepted. The equilibrium in which all messaged players accept one of the images and reject the other gives messaged players a larger expected payoff, but there is no way they can coordinate their choices. Hence, the equilibrium in which both images are accepted, which for messaged players Pareto-dominates the equilibrium in which both images are rejected, seems salient. The supporting beliefs are easily constructed. The only remaining case is the one in which Λ ≤ Λic = Λid < Λ ′ . In this case if both images were accepted in stage 1 they would not be validated in stage 2, so "accept both images" is not an equilibrium. "Accept one image but not the other is an equilibrium", but there is no way for messaged players to coordinate their choices. We therefore propose the equilibrium in which neither image is accepted. Here too the supporting beliefs are easily constructed. To explore the associated demand functions, let E = f (Λ) and E ′ = f (Λ′) . We will focus on the demand for costume c. If Edi < Λ , demand for costume c is given by equation (6) above. Assume then that Edi ≥ Λ . One important thing to notice is that there is then a non-concavity in Qc ( Eci , E di ) at Eci = Edi . Regardless of the magnitude of Eci , costume c will get fraction 1/M of the custom of ummessaged players, so focus on the choices of messaged players. For Eci < Edi , costume c will get fraction 1/(M - 1) of the custom of messaged players of types other than i. And for Eci > E di , costume c will get all the custom of all messaged players of type i. Given the assumption that pi > 1(M - 1), we see that demand for good c increases discretely as Eci passes
23
through Edi : in other words, the limit of Qc ( Eci , Edi ) as Eci approaches Edi from above exceeds the limit of Qc ( Eci , Edi ) as Eci approaches Edi from below. What happens when Eci = E di depends on the value of Edi relative to Λ ′ : if it is less than Λ ′ , neither image will be accepted and costume c will get the custom of fraction 1/M of all messaged players; if it is larger than Λ ′ , costume c will get the custom of 1/2 of the messaged players of type i. In either case, the limit of Qc ( Eci , Edi ) as Eci approaches Edi from above exceeds Qc ( Eci , Edi ) , evaluated at Eci = E di . Another important thing to notice is that a little bit of image advertising does nothing. That is, Qc ( Eci , E di ) is independent of Eci when Eci < E di .
Let us turn briefly to the game in which competing firms choose the amount to spend on image advertising, assuming still that their costume prices are parametric and identical. An immediate implication of the non-concavity in the demand functions is that there is only one possible equilibrium in which two firms establish the same image for their goods -- both firms must saturate the target market. There is absolutely no point in spending less than one's competitor on image advertising since it can have no effect on demand. And it cannot be an equilibrium to spend the same amount as one's competitor since an infinitesimal increase in expenditure will discretely increase demand. Unless, of course, Λic = Λi d = 1; that is, unless both firms have saturated the target group.
The analysis of this section generalizes immediately to the case in which more than 2 firms try to establish the same image for their costumes. In particular: there is a non-concavity in own quantity demanded as a function of own amount spent on image advertising at the point where own amount is equal to the largest amount spent by one's competitors; own quantity demanded is independent of own amount spent when a firm spends less than the largest amount spent by its competitors; in the game where firms non-cooperatively choose expenditures on image advertising, the only possible equilibrium is the one in which all farms saturate the target group.
24
IV. Discussion
As we see it, the following are the important features of our theory of image advertising. First, the target group for an image campaign is necessarily larger that the group of intended buyers of the good, for the target group includes as well the target audience of the intended buyers -- the group of people with whom the buyers want to communicate through their purchase and use of the image good. Second, to be effective, an image campaign must convince some of the intended buyers that a substantial portion of their target audience have received and understood the good's intended image; hence, a little bit of image advertising is bound to be ineffective. Successful image campaigns are massive. Third, if two or more goods attempt to establish the same image, the advertising campaigns will achieve virtual saturation of the target group.
Consistent with all three features,, image advertising campaigns are frequently associated with very wide coverage. Moreover, discussions with media practitioners suggest that firms are willing to pay a premium to assure that image ads are coordinated and reach large groups of consumers simultaneously. Thus, they may be willing to pay high up front rates for advance purchase of TV, air time, or print media to assure that slots for image ads are locked in, even though rates for spot advertising based on current availability are significantly lower.
Saturation aspects of image advertising are also evident in the projection of images far beyond immediate purchasers of a good. One well publicized example is the recent controversial "Old Joe" campaign for Camel cigarettes launched in 1988, which critics claim was aimed at youths Pierce et al. 1991). In 1990 about 26% of the U.S. population over 18 smoked. Reported use of cigarettes by youths 12 to 18 was about 12% (National Center for Health Statistics 1992). Among smokers, Camels market share has historically been modest, although growing recently (under 5% of smoking adults in 1986; 8.1 % of teenage smokers in a 1989 survey) (Centers for Disease Control 1991, 1992). Nevertheless, a 1991 survey of high school students in selected states indicated that over 97% had seen "Old Joe" and 93% knew the Camel brand. The analogous figures for adults were 72% and 57% (DiFranza et al. 1991). Thus, although a minority of the population smoked at all and only a tiny fraction of the population smoked Camels, the "Old Joe" campaign reached virtually all of the youths surveyed and a majority of
25
adults. In this regard, the image campaigns associated with the introduction of the Lexus and Infinity automobiles are instructive. Both cars are intended for buyers with annual incomes in excess of $100,000, yet both campaigns were massive and broad based. The North American advertising budget for each of the cars in the year in which it was launched was more than $125,000,000. To put this in perspective, the total North American advertising budget for The Honda Corporation in a typical year is only $125,000,000. And TV ads for both cars were broadcast in connection with a number of popular programs, watched by a wide variety of viewers.
26
References
Cafferata, Patricia, and Tybout, Alice M., (eds) Cognitive and Affective Responses to Advertising. (Lexington, MA: D.C. Heath, 1989).
Jack L. Carr and Janet T. Landa "The economics of symbols, clan names, and religion." Journal of Legal Studies 22:1 (1983) 135- 154.
DiFranza, Joseph R. et al., "RJR Nabisco's Cartoon Camel Promotes Camel Cigarettes to Children." Journal of the American Medical Association 266:22 (1991) 3149-3153.
Eaton, B. Curtis and Jasmina Arifovic (1998)
Frank, Robert H, Passions Within Reason. (New York: W.W. Norton, 1988).
Jones, Stephen R.G. , The Economics of Conformism (Oxford, Basil Blackwell 1984)
Kihlstrom, Richard E., and Riordan, Michael H. "Advertising as a Signal”. Journal of Political Economy 92 (June 1984) 427-50.
Klein, Benjamin, and Leffler, Keith, "The Role of Market Forces in Assuring Contractual Performance." Journal of Political Economy 94 (August 1981) 615-641.
Centers for Disease Control. "Cigarette Brand Use Among Adult Smokers- United States." Morbidity and Mortality Weekly Report 76 (1990) 665-667.
Centers for Disease Control "Comparison of the Cigarette Brand Preferences of Adult and Teenaged Smokers- United States, 1989, and 10 U.S. Communities, 1988 and 1990." Morbidity and Mortality Weekly Report 41:10 (1992) 169-173.
27
National Center for Health Statistics, Health United States 1991. U. S. Public Health Service 1992.
Nelson, Phillip. "Advertising as Information." Journal of Political Economy 82 (July/August 1974) 729-54.
Pierce, John P. et al. "Does Tobacco Advertising Target Young People to Start Smoking?" Journal of the American Medical Association 266:22 (1991) 3154-58.
Spence, Michael A., Market Signaling: Informational Transfer in Hiring and Related Screening Processes. (Cambridge MA: Harvard University Press, 1974).
Wintrobe, Ronald, "Taxing Altruism." Economic Inquiry 21 (1983) 255-70.
28
