We introduce a new solution conceptcalled maximin equilibrium which extends von Neumann's maximin strategy idea to n-player non-cooperative games by incorporating common knowledge of 'rationality' of the players. Our rationality assumption is , however, stronger than the one of maximin strategy and weaker than the one of Nash equilibrium. Maximin equilibrium, just like maximin strategies, is a method for evaluating the uncertainty that players are facing by playing the game. We show that maximin equilibrium is invariant under strictly increasing transformations of the payoff functions. Notably, every finite game possesses a maximin equilibrium in pure strategies. Considering the games in von Neumann and URLenstern mixed extension, we show that maximin equilibrium is a generalization of Nash equilibrium . In addition, we demonstrate that maximin equilibria and Nash equilibria coincide in two-player zero-sum games. We propose a refinement of maximin equilibrium called strong maximin equilibrium. Accordingly, we show that for every Nash equilibrium that is not a strong maximin equilibrium there exists a strong maximin equilibrium that Pareto dominates it. In addition, no strong maximin equilibrium is ever Pareto dominated by a Nash equilibrium. Finally, we discuss maximin equilibrium predictions in several games including the traveler's dilemma .
Cooperation among individuals has been one of the most puzzling phonemena in economics and other social sciences. In this paper, I introduce a novel solution concept, dubbed the optimin criterion, which (to the best of my knowledge) is the first parameter-free concept that can selectively explain the direction of well-established non-Nash deviations towards cooperation in games, including the repeated prisoner's dilemma, the traveler's dilemma, the centipede game, and the repeated public goods game. Moreover, the optimin criterion generalizes and unifies results in various fields: It not only coincides with (i) Wald's statistical decision-making criterion when Nature is antagonistic, (ii) the core in cooperative games when the core is nonempty, though it exists even if the core is empty, but also generalizes (iii) Nash equilibrium in n-person constant-sum games, (iv) stable matchings in matching models, and (v) competitive equilibrium in the Arrow-Debreu economy. Moreover, every Nash equilibrium satisfies the optimin criterion in an auxiliary game .
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We introduce a new solution conceptcalled maximin equilibrium which extends von Neumann's maximin strategy idea to n-player non-cooperative games by incorporating common knowledge of 'rationality' of the players. Our rationality assumption is , however, stronger than the one of maximin strategy and weaker than the one of Nash equilibrium. Maximin equilibrium, just like maximin strategies, is a method for evaluating the uncertainty that players are facing by playing the game. We show that maximin equilibrium is invariant under strictly increasing transformations of the payoff functions. Notably, every finite game possesses a maximin equilibrium in pure strategies. Considering the games in von Neumann and URLenstern mixed extension, we show that maximin equilibrium is a generalization of Nash equilibrium . In addition, we demonstrate that maximin equilibria and Nash equilibria coincide in two-player zero-sum games. We propose a refinement of maximin equilibrium called strong maximin equilibrium. Accordingly, we show that for
Cooperation among individuals has been one of the most puzzling phonemena in economics and other social sciences. In this paper, I introduce a novel solution concept, dubbed the optimin criterion, which (to the best of my knowledge) is the first parameter-free concept that can selectively explain the direction of well-established non-Nash deviations towards cooperation in games, including the repeated prisoner's dilemma, the traveler's dilemma, the centipede game, and the repeated public goods game. Moreover, the optimin criterion generalizes and unifies results in various fields: It not only coincides with (i) Wald's statistical decision-making criterion when Nature is antagonistic, (ii) the core in cooperative games when the core is nonempty, though it exists even if the core is empty, but also generalizes (iii) Nash equilibrium in n-person constant-sum games, (iv) stable matchings in matching models, and (v) competitive equilibrium in the Arrow-Debreu economy. Moreover,
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that is not a strong maximin equilibrium there exists a strong maximin equilibrium that Pareto dominates it. In addition, no strong maximin equilibrium is ever Pareto dominated by a Nash equilibrium. Finally, we discuss maximin equilibrium predictions in several games including the traveler's dilemma
satisfies the optimin criterion in an auxiliary game