Information Asymmetric Cooperative Games with Agreements Self-Implemented (Contemporary Mathematics, 2025)
This paper introduces asymmetric information into the analysis of cooperative games with agreements self-implemented, establishes theoretical models of a one-shot information asymmetric cooperative game with agreements self-implemented, aims to provide analytical tools for the study of political science, economics, sociology, and other humanities disciplines. In an information asymmetric cooperative game with agreements self-implemented, the players make their decisions through their virtual games on the basis of their own information sets. By introducing the virtual games of the players, this paper defines the coalition equilibrium of an information asymmetric cooperative game with agreements self-implemented and examines the condition for its existence. This paper demonstrates that in an information asymmetric cooperative game with agreements self-implemented, the condition for the existence of its coalition equilibrium is that information is symmetric after the game is completed. This paper defines the distribution equilibrium of the cooperative payoff of a coalition in the coalition equilibrium (if it does exist) as the Nash equilibrium of the bargaining game between the core members of the coalition. When the core members are unallied in the bargaining game, the distribution of a coalition member is the sum of his cooperative payoff distribution when the estimations of the optimal strategic combination choice of all the core members are all correct and the distribution he gets in the "misjudgment" cooperation; when the core members are allied in the bargaining game, the distribution of a cooperative team is the sum of its cooperative payoff distribution when the estimations of the optimal strategic combination choice of all teams are all correct and the distribution it gets in the "misjudgment" cooperation.
Keywords: information asymmetry; information asymmetric cooperative game with agreements self-implemented; virtual game; coalition equilibrium; bargaining game; core coalition; extensive coalition