Characteristic Function of Maxmax Defensive-Equilibrium Representation for TU-Games with Strategies

In this paper, we propose a characteristic function of the maxmax defensive-equilibrium representation that maps every TU-game with strategies to a TU-game. This characteristic function is given by a two-step procedure in which each of any two complementary coalitions successively selects the equilibrium in a way that maximizes its utility. We then investigate the properties of this characteristic function and present the relations of the cores under three characteristic functions. Finally, as applications of our findings, we provide a firm production advertising game, a supply chain network game, a cost game with strategies, and a Cournot game.

Automated summary

In this paper, a characteristic function is proposed to map each TU-game with strategies to a TU-game. The characteristic function is obtained through a two-step procedure where each complementary coalition successively selects the equilibrium that maximizes its utility. The properties of this characteristic function are then investigated, along with the relations of the cores under three characteristic functions. Furthermore, several applications of these findings are provided, including a firm production advertising game, a supply chain network game, a cost game with strategies, and a Cournot game.