ratio 50 schedule of reinforcement while obtaining additional food according to either ... The various combinations of within-session earned and unearned food, ...
1993, 59, 231-243
JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR
NUMBER
1
(JANUARY)
RESPONSE-REINFORCER INDEPENDENCE AND THE ECONOMIC CONTINUUM: A PRELIMINARY ANALYSIS ABDULRAZAQ A. IMAM WEST VIRGINIA UNIVERSITY
Three pigeons were exposed to 1-hr and 4-hr sessions during which they earned food under a fixedratio 50 schedule of reinforcement while obtaining additional food according to either a variableinterval or a variable-time schedule. Postsession food was provided after the 1-hr sessions. The frequency of the variable-interval and variable-time food presentations was varied under the two session durations. The various combinations of within-session earned and unearned food, as well as the postsession food, defined conditions on the open-to-closed economy continuum. Key pecks tended to increase as the frequency of either variable-interval or variable-time food decreased. An economiccontinuum analysis based on an independence quotient as a measure of response-reinforcer independence is presented to account for the effects. Key words: closed economy, open economy, economic continuum, independence quotient, response patterns, variable-time schedule, fixed-ratio schedule, concomitant schedules, conjoint schedules, key peck, pigeons
Extensive empirical support for the distinction between open and closed economies has been reported (e.g., Collier, Hirsh, & Hamlin, 1972; Mazur, 1983). In an open economy, a subject's access to a commodity (e.g., food) is determined by the experimenter either holding daily within-session consumption constant or providing additional performance-independent food outside of experimental sessions. By contrast, in a closed economy, within-session performance determines total daily food intake (Collier, 1983; Hursh, 1980). The distinction, therefore, is based in part on the presence or absence of extrasession performance-independent food. In distinguishing between the two types of economy, Hursh observed:
daily consumption and the equilibrium conditions, while others may be strictly open in the sense that daily consumption is totally independent of behavior under the test conditions. (1980, p. 223)
Hursh's observations suggest that there are degrees of "openness" and "closedness' of economies determined by the degree of constraint placed upon food consumption in a given situation. In modeling the relative constraints of a particular economy, the proportion of the total food consumption that is performance independent is an important factor. The greater the proportion, the more independence exists between behavior and total consumption. Availability of a substitutable source of a commodity within or outside the session contribThe concept of open [and closed] economies utes to the independence between consumption probably defines a continuum. Specific arand behavior, and therefore should help define rangements of between-session feeding and the economy (see Hursh & Bauman, 1987). control of session length would include condiTo determine the degree of openness of the tions that are very nearly closed in providing economy, the proportion of within-session unonly a small degree of independence between earned food (or Wj) and postsession unearned food (or Pj) may be combined to represent the Portions of these data were collected as part of a doctoral proportionality of performance-inaggregate dissertation submitted by the author to the College of Arts and Sciences at West Virginia University. The data were dependent food. This aggregate measure, or presented at the 1989 meeting of the Association for Be- independence quotient (IDQ), can be exhavior Analysis in Milwaukee, Wisconsin. I thank Greg pressed comments on Galbicka and Andy Lattal for their helpful
an earlier version of the paper. Reprints may be obtained from the author, now at the Department of Medical Neu-
IDQ=P.+ W.
rosciences, Walter Reed Army Institute of Research, Washington, D.C. 20307-5100.
c,
231
(1)
232
ABDULRAZAQ A. IMAM
where T, is the total daily consumption. IDQ, then, is determined by a composite of food sources that constitutes total food consumption. The IDQ is conceptually useful because its value (ranging between 0, for complete dependence between food consumption and performance, and 1, for complete independence between food consumption and performance) changes as the economy is altered by the presence or absence of either type of unearned food. As IDQ approaches 1, the economy becomes more open; as IDQ approaches 0, the economy becomes more closed. As a single value, IDQ is an index of substitutability (the higher the IDQ, the higher the degree of substitutability) that represents economic conditions on the open-to-closed economy continuum. Figure 1 shows a number of economic conditions theoretically possible from various combinations of within-session and postsession unearned food, as well as within-session earned food or (We). Until recently, the most widely studied case is the open economy (Case D; 0 < IDQ < 1, with Pu > 0). Increasingly, the strictly closed economy (Case A; IDQ = 0, with TC = We and P, = 0) is being studied (e.g., Collier, 1983). The last condition (Case E), for which IDQ = 1, is rarely, if ever, studied in behavioral research. Of the three cases with 0 < IDQ < 1, only the open economy has been analyzed in terms of mapping the continuum of conditions defined by varying the amounts of postsession food. Although the role of performance-independent extrasession food in defining the economy (e.g., Collier, 1983; see Hursh, 1980) and mapping the economic continuum (e.g., Hursh, Raslear, Bauman, & Black, 1989) has been addressed experimentally, the economic role of within-session response-independent food delivery in defining or mapping the economic continuum remains unexamined. Previous studies of within-session response-independent food delivery have been conducted in open economies (e.g., Green, Kagel, & Battalio, 1987; Imam & Lattal, 1988; Lattal & Bryan, 1976; Zeiler, 1979), but the degree of "openness" or "closedness" of these economies cannot be ascertained because data on the amount of postsession feeding were not reported. Response rate typically increases as the frequency of within-session response-independent food declines (e.g., Lattal & Bryan, 1976; Zeiler,
1979).
The present study attempted to assess the effect of varying the frequency of within-session response-independent food delivery in otherwise open and closed economies while monitoring the amount of extrasession food in the open economy. Concomitant schedules combining response-independent and response-dependent grain presentations and conjoint schedules of reinforcement (see Imam & Lattal, 1992) were used. The schedules enabled the manipulation of both the availability and the frequency of response-independent food within the test sessions. In conjunction with extrasession feeding, the schedules defined the economic conditions studied. The conditions included Cases A, B, C, and D shown in Figure 1. The degree to which combinations of these sources of food contribute to total food consumption should determine the response output. For example, under a strictly open economy, during which an animal obtains all its food independent of within-session performance, little or no responding would occur. On the other hand, in a strictly closed economy, during which an animal must earn all its food intake by responding, a considerable amount of responding would occur. Between these two extremes, some of the food may be earned, some may be obtained freely either within or outside the test situation, or some may be obtained both within and outside the test situation. Intermediate economic conditions established by these various combinations of food sources should engender intermediate levels of responding. In the present experiment, combinations of response-dependent and response-independent food within test sessions of 1-hr or 4-hr durations were used to explore the economic conditions established with and without postsession feeding.
METHOD
Subjects Three White Carneau pigeons, previously used in studies of schedules of reinforcement, were maintained initially at their free-feeding body weights. Water and health grit were available at all times in individual home cages. Apparatus Two standard experimental chambers (30 cm by 32 cm by 37.2 cm) were used. Sessions for P2923 were conducted in one, and those
ECONOMIC CONTINUUM
Food Sources
Fo o d__ourc_e_s__ EXTERNAL Case A
TEST SESSION
TLc
=We
P
Tc=We+Wl_
", 0
I
e
B
90,
: "
T~~W e+1K~~ T=W +W,- , 0W 0 uZ
1% =0
Case C
233
Terms of
&
Value
IDQ
IDQ=(Pu+Wu)/Tc IDQ
P
_______ I
(Ca |IDQ=
0
