Ismail, Mehmet (2014): Maximin equilibrium.

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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 NeumannMorgenstern 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. (Submitted to MPRA for stable archival purposes. This is the Maastricht GSBE version.)
Item Type:  MPRA Paper 

Original Title:  Maximin equilibrium 
Language:  English 
Keywords:  Noncooperative games, maximin strategy, zerosum games 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  97322 
Depositing User:  Mehmet Ismail 
Date Deposited:  04 Dec 2019 13:32 
Last Modified:  04 Dec 2019 13:32 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/97322 