A Game Theoretic-Mathematical Programming Analysis of Cooperative Phenomena in Oligopolistic Markets

This paper investigates cooperative behavior in an industry that supplies a homogeneous product and consists of oligopolistic firms. The analysis is conducted within a game theoretic framework in which each firm is viewed as a player whose strategy is its level of production. By defining a suitable characteristic function that evaluates the worth of each possible coalition, we attempt to quantify the individual and collective bargaining powers of firms in order to predict merger or contractual agreements and production strategies. In particular, we define three games via three characteristic functions, each of which is based upon some assumed market behavior on the part of the players. For each game, we investigate whether the firms would choose to remain separate or form a grand coalition or some other coalition structure. For some insightful special cases, we are able to establish the resulting outcome and assert whether a core allocation of profits among members of an emerging coalition exists and whether the Shapley value allocation belongs to the core. In the more general case, we use the U.S. copper industry as an example to illustrate how Shapley values may be used to determine possible emerging coalition structures.