Maximin equilibrium

Ismail, Mehmet (2014): Maximin equilibrium.

Abstract

We introduce a new concept which extends von Neumann and Morgenstern's maximin strategy solution by incorporating `individual rationality' of the players. Maximin equilibrium, extending Nash's value approach, is based on the evaluation of the strategic uncertainty of the whole game. We show that maximin equilibrium is invariant under strictly increasing transformations of the payoffs. Notably, every finite game possesses a maximin equilibrium in pure strategies. Considering the games in von Neumann-Morgenstern mixed extension, we demonstrate that the maximin equilibrium value is precisely the maximin (minimax) value and it coincides with the maximin strategies in two-person zerosum games. We also show that for every Nash equilibrium that is not a maximin equilibrium there exists a maximin equilibrium that Pareto dominates it. Hence, a strong Nash equilibrium is always a maximin equilibrium. In addition, a maximin equilibrium is never Pareto dominated by a Nash equilibrium. (Submitted to MPRA for stable archival purposes. This is the Maastricht GSBE version.)

• Item Type: MPRA Paper
• Language: English
• Keywords: Non-cooperative games, maximin strategy, zerosum games
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

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