COALITIONAL BELIEFS IN COURNOT OLIGOPOLY TU GAMES

摘要

In cooperative games, due to computational complexity issues, deviant agents are not able to base their behavior on the outsiders' status but have to follow certain beliefs as to how it is in their strategic interest to act. This behavior constitutes the main interest of this paper. To this end, we quantify and characterize the set of coalitional beliefs that support cooperation of such agents. Assuming that they are engaged in a differentiated Cournot competition, for every belief of the deviants we define a TU-game, the solution to which characterizes the set of coalitional beliefs that support core nonemptiness. For this we fix the number of coalitions that deviants S will face to, say, j in number and introduce the notion of j-belief~a of S as the least number of coalitions into which the outsiders NS will reorganize. We then define for every j-belief a TU-game and the j-belief core of it. We prove that the worth of S is minimized when the n - s agents split approximately equally among the j coalitions, while the worth of S is maximized when j - 1 agents have one member and one coalition has n - s - (j - 1) members. Given the above, we prove that when goods are substitutes, the j-belief core is nonempty, provided that S believe the N﹨S will form a sufficiently large number of coalitions, while when goods are complements, the j-belief core is nonempty irrespective of the beliefs of the agents in S. Finally, in the case of homogeneous goods we prove that the j-belief core is nonempty and depends only on the number of the outsider coalitions and not on their size.