(untitled) (Contemporary Mathematics, 2024)
This paper introduces asymmetric information into the analysis of cooperative games with agreements implemented by a third party and establishes theoretical models of a one-time information asymmetric cooperative game with agreements implemented by a third party for the first time, using the methodology proposed in previously done research studying coalition formation and cooperative payoff distribution. In an information asymmetric cooperative game with agreements implemented by a third party, players may retain their own private information, and make decisions through their virtual games on the basis of their own information sets. This paper defines the virtual cooperative games of the players and demonstrates the equilibrium of the virtual cooperative game of a player; proposes the condition for the existence of the coalition equilibrium in an information asymmetric cooperative game with agreements implemented by a third party, defines and provides the existence proof of this coalition equilibrium when it does exist; defines the public choice game of a coalition on the strategic combination choice in a certain coalition situation, defines and provides the existence proof of the equilibrium of this game; examines the condition for the existence of the bargaining game on the distribution of the cooperative payoff of a coalition, defines and provides existence proof of the bargaining game, when the coalition members are allied or unallied in the bargaining game.