Cooperative Games with Agreements Self-Implemented (Contemporary Mathematics, 2025)
In classical cooperative game theory, it is often assumed that agreements are implemented by a third party, this paper provides an analytical framework for cooperative games with agreements self-implemented in three scenarios: (1) the possible opportunistic behaviors in the distribution process are ignored; (2) coalitions centralize all the payoffs their members get in the game to inhibit the possible opportunistic behaviors in the distribution process; (3) coalitions distribute their cooperative payoffs before the game begins to inhibit the possible opportunistic behaviors in the distribution process. In each scenario, this paper examines the formation of the coalitions and the distribution process of the cooperative payoff of a coalition, defines and provides the existence proof of the coalition equilibrium of a cooperative game with agreements self-implemented, defines and provides the existence proof of the equilibrium in the bargaining game of a coalition on the distribution of its cooperative payoff, when its members cooperate in the game or not.
Keywords: cooperative game; self-implemented agreement; coalition equilibrium; escape-payoff deriving from deviation; common payoff; bargaining game