We introduce a new theory of games which extends von Neumann's theory of zero-sum games to nonzero-sum games by incorporating common knowledge of individual and collective 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  URLenstern mixed extension, we demonstrate that the maximin equilibrium value is precisely the maximin (minimax) value and it coincides with the maximin strategies in two-player zero-sum games. We also show that for every Nash equilibrium that is not a  maximin equilibrium there exists a  maximin equilibrium that Pareto dominates it. 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.
We introduce a new solution concept called 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.
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theory of games
solution concept called maximin equilibrium
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theory of zero-sum games to nonzero-sum
maximin strategy idea to n-player non-cooperative
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individual and collective rationality
'rationality'
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Our rationality assumption is, however, stronger than the one of maximin strategy and weaker than the one of Nash equilibrium.
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extending Nash's value approach, is based on the evaluation of the strategic uncertainty of the whole
just like maximin strategies, is a method for evaluating the uncertainty that players are facing by playing the
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payoffs
payoff functions
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Neumann and
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demonstrate that the maximin equilibrium value is precisely the maximin (minimax) value and it coincides with the maximin strategies
show that maximin equilibrium is a generalization of Nash equilibrium. In addition, we demonstrate that maximin equilibria and Nash equilibria coincide
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also
propose a refinement of maximin equilibrium called strong maximin equilibrium. Accordingly, we
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strong
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strong
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a
no strong
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never
ever