Competition and collusion in bilateral markets

In this paper, the core of a market game which constitutes the set of equilibria in the process of competitive contracting and recontracting is criticized as a solution concept for not being immune against theory absorption in the sense that knowledge of the core on part of the traders may result in a collusive stabilization of some dominated imputation. It is pointed out that a stable set (or, von Neumann-Morgenstern) solution does not suffer from this deficiency. Moreover, it is argued that stable set solutions provide an adequate analytical framework for the study of collusion, and are in this respect superior to the approach (relying on the core concept) chosen by Aumann in his work on disadvantageous monopolies. For symmetric bilateral market games — generated by markets involving the exchange of only two commodities, one of which also serves as a means of side payment and utility transfer, among two types of traders — with one seller and one up to three buyers all symmetric solutions are determined. Furthermore, a symmetric solution for markets with equal, but otherwise arbitrary, numbers of sellers and buyers is given. The symmetric stable sets of imputations are interpreted as rational standards of behavior providing the consistent and defensible rules of division necessary to make a cartel agreement viable.This research was partially supported by a grant given to New York University, Department of Economics, by the Office of Naval Research. (# N00014-76-C-0033). A first version of the paper was presented at the Third World Congress of the Eeconomtric Society, Toronto, Aug. 20–26, 1975, under the title Symmetric Solutions of Bilateral Market Games.