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2018•Discrete Dynamics in Nature and SocietyOpen access

A Note on Strategic Stability of Cooperative Solutions for Multistage Games

Lei Wang, Cui Liu, Juan Xue, Hongwei Gao

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Abstract

The problem of strategic stability of cooperative solutions for multistage games is studied. The sufficient conditions related to discount factors are presented, which guarantee the existence of Nash or strong Nash equilibria in such games and therefore guarantee the strategic stability of cooperative solutions. The deviating payoffs of players are given directly, which are related closely to these conditions and avoid the loss of super-additivity of a class of general characteristic functions. As an illustration, Nash and strong Nash equilibria are found for the repeated infinite stage Prisoner’s dilemma game.

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The problem of strategic stability of cooperative solutions for multistage games is studied. The sufficient conditions related to discount factors are presented, which guarantee the existence of Nash or strong Nash equilibria in such games and therefore guarantee the strategic stability of cooperative solutions. The deviating payoffs of players are given directly, which are related closely to these conditions and avoid the loss of super-additivity of a class of general characteristic functions. As an illustration, Nash and strong Nash equilibria are found for the repeated infinite stage Prisoner’s dilemma game.

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Available abstract

The problem of strategic stability of cooperative solutions for multistage games is studied. The sufficient conditions related to discount factors are presented, which guarantee the existence of Nash or strong Nash equilibria in such games and therefore guarantee the strategic stability of cooperative solutions. The deviating payoffs of players are given directly, which are related closely to these conditions and avoid the loss of super-additivity of a class of general characteristic functions. As an illustration, Nash and strong Nash equilibria are found for the repeated infinite stage Prisoner’s dilemma game.

Key concepts: Nash equilibrium, Mathematical economics, Stability (learning theory), Additive function, Dilemma, Class (philosophy), Epsilon-equilibrium, Best response

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