Stable Cartels Revisited

Abstract

This paper analyzes cartel stability when firms are farsighted. It studies a price leadership model a la D' Aspremont et al. (1983), where the dominant cartel acts as a leader by determining the market price, while the fringe behaves competitively. According to D'Aspremont et al.'s (1983) approach a cartel is stable if no firm has an incentive to either enter or exit the cartel. In deciding whether to deviate or not, a firm compares its status quo with the outcome its unilateral deviation induces. However, the firm fails to examine whether the induced outcome will indeed become the new status quo that will determine its profits. Although the firm anticipates the price adjustment following its deviation, it ignores the possibility that more firms may exit (or enter) the cartel that may eventually stabilize in a very different situation from the one the firm riginally induced. In other words, the firm does not consider the fact that the outcome immediately induced by its deviation may not be stable itself. We propose a notion of cartel stability that allows firms to fully foresee the result of their deviation. Our solution concept is built in the spirit of von Neumann and Morgenstern's (1944) stable set, while it modifies the dominance relation following Harsanyi's (1974) criticism. We show that there always exists a unique, non-empty set of stable cartels and provide an algorithm the determines it.