Maximin equilibrium

M.S. Ismail

Research output: Working paper / PreprintWorking paper

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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 twoperson 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. Finally, we discuss maximin equilibrium predictions in several games including the traveler's dilemma.
Original languageEnglish
Place of PublicationMaastricht
PublisherMaastricht University, Graduate School of Business and Economics
Publication statusPublished - 1 Jan 2014

Publication series

SeriesGSBE Research Memoranda


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