Testing Models of Pure Exchange

Abstract

We reanalyze the experimental data of Michener et al. (1975, 1977) to explain behavior in pure exchange situations. The data were compared to predictions of various cooperative bargaining models and to the predictions of a bilateral exchange model developed in the present paper. The bilateral exchange model fitted well and performed best. The model could explain asymmetries in actors' exchange outcomes as commonly observed in exchange networks, and that generalized exchange hardly occurred in the experiments. However, systematic deviations from predictions of the bilateral exchange model and other models of rational behavior were observed; actors tend to focus on their absolute preferences rather than on their relative preferences. These deviations could be explained by a boundedly rational model of exchange, assuming that actors use heuristics to detect profitable exchange opportunities.

Keywords:

• bounded rationality
• cooperative game theory
• exchange
• heuristics
• task complexity

Notes

¹This definition of an exchange situation is similar to Nash's (1950, p. 155) definition of a two-person bargaining situation.

Note. Actors A, B can exchange their initial endowments X, Y. C denotes the initial endowment, I the utility of one unit of an endowment.

²Psychologist Emerson (e.g., 1962, 1976) formulated power-dependence theory on the basis of the EG solution to predict outcomes of bilateral exchange and exchange in small groups of actors. Although initially social scientists concentrated on pure exchange, their attention rapidly shifted to the study of exchange as represented by splits of common resource pools. Most of that work concerns the bilateral exchanges between pairs of actors contained in networks, so-called exchange networks. For instance, see Willer (1999) for a description of the large body of research on network exchange.

³In theory, some models of cooperative bargaining, like Nash or equal utility gain, can select more than one solution (e.g., see Heckathorn, 1978). However, always one solution is selected in the pure exchange situations here because of the linearity of the payoff space. For an explanation of the set of requirements underlying the Nash and RKS bargaining solutions, see Luce and Raiffa (1957) and Felsenthal and Diskin (1982).

⁴Assuming linear payoffs, payoff spaces of bilateral pure exchange situations in which one good is exchanged for one other good either have one kink or no kink. It can be shown that the Nash and RKS solutions are always equal if there is no kink, and are equal only under certain conditions if there is a kink.

Note. Names of colors and Greek characters represent endowments and actors, respectively.

Note. Names of colors and Greek characters represent endowments and actors, respectively.

⁵We do not include the core sets here because they are not easy to visualize, and since they are big sets the core prediction is quite uninformative about the final outcome of the pure exchange situation.

Note. The square root of the unexplained variances (SD) of each configuration is presented in the top row. “Average” represents the average of the variance explained in a row or column.

Note. The first columns represent the number of opportunities of types D ₀, S ₀, D _b , S _b in each configuration on the basis of initial and, between brackets, final allocations. The last columns represent the total potential gains from bilateral exchange for each situation on the basis of fin(al) and ini(tial) allocations.

⁶There were in total 3 × 3 × 6 + 3 × 6 × 10 = 234 actor-good pair combinations (for each paper these numbers represent configurations × actor pairs × good pairs).

⁷Using the hypergeometric distribution, the probability of obtaining 3 or 4 complex type exchanges in a sample of 13 from a population of 88 with 4 complex type is equal to .

⁸Using the hypergeometric distribution, the probability of obtaining 2 or less D ₀ exchanges in a sample of 10 from a population of 84 with 57 of type D ₀ is equal to

⁹The predictions of the P model were unreasonable for this configuration, and performance bad, because it predicted Alpha to lose points.