Cooperative Game with Agreements Implemented by a Third Party

Abstract

In the literature of cooperative game theory, it is often assumed that there is only one coalition composed of all the players other than the dummies in a cooperative game of complete information, although the coalition formation is examined and the equilibrium process of coalition formation (EPCF) was defined in a repeated cooperative game of incomplete information. On the other hand, the blocking approach only provided several possible ranges of the distribution scheme of the cooperative payoff of a coalition in a cooperative game with agreements implemented by a third party, and the single point solutions provided are usually collectivistic. This paper examines the coalition formation in a cooperative game with agreements implemented by a third party, and provides the existence proof and an algorithm of the coalition equilibrium; moreover, this paper analyzes the equilibrium of the bargaining game on the distribution of the cooperative payoff of a coalition under the coalition equilibrium, and examines the distribution scheme of cooperative payoff of a coalition.