Satoh, Atsuhiro and Tanaka, Yasuhito (2017): Maximin and minimax strategies in symmetric multiplayers game with two strategic variables.
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Abstract
We examine maximin and minimax strategies for players in symmetric multiplayers game with two strategic variables. We consider two patterns of game; the xgame in which strategic variables of players are x's, and the pgame in which strategic variables of players are p's. We will show that the maximin strategy and the minimax strategy in the xgame, and the maximin strategy and the minimax strategy in the pgame for the players are all equivalent. However, the maximin strategy for the players are not necessarily equivalent to their Nash equilibrium strategies in the xgame nor the pgame. But in a special case, where the objective function of one player is the opposite of the sum of the objective functions of other players, the maximin and the minimax strategies for the players constitute the Nash equilibrium both in the xgame and the pgame.
Item Type:  MPRA Paper 

Original Title:  Maximin and minimax strategies in symmetric multiplayers game with two strategic variables 
Language:  English 
Keywords:  multiplayers game, two strategic variables, maximin strategy, minimax strategy 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games D  Microeconomics > D4  Market Structure, Pricing, and Design > D43  Oligopoly and Other Forms of Market Imperfection 
Item ID:  76353 
Depositing User:  Yasuhito Tanaka 
Date Deposited:  22 Jan 2017 14:48 
Last Modified:  07 Oct 2019 18:08 
References:  Matsumura, T., Matsushima,N. and Cato,S. (2013), ``Competitiveness and R&D competition revisited'' Economic Modelling, 31, 541547. Satoh, A. and Tanaka, Y. (2013), ``Relative profit maximization and Bertrand equilibrium with quadratic cost functions,'' Economics and Business Letters, 2, pp. 134139. Satoh, A. and Tanaka, Y. (2014a), ``Relative profit maximization and equivalence of Cournot and Bertrand equilibria in asymmetric duopoly,'' Economics Bulletin, 34, pp. 819827. Satoh, A. and Tanaka, Y. (2014b), ``Relative profit maximization in asymmetric oligopoly,'' Economics Bulletin, 34, 16531664. Satoh, A. and Tanaka, Y. (2016), ``Symmetric multiperson zerosum game with two sets of strategic variables,'' mimeo. Tanaka, Y. (2013a), ``Equivalence of Cournot and Bertrand equilibria in differentiated duopoly under relative profit maximization with linear demand,'' Economics Bulletin, 33, 14791486. Tanaka, Y. (2013b), ``Irrelevance of the choice of strategic variables in duopoly under relative profit maximization,'' Economics and Business Letters, 2, pp. 7583. VegaRedondo, F. (1997), ``The evolution of Walrasian behavior'' Econometrica 65, 375384. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/76353 
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Maximin and minimax strategies in symmetric oligopoly: Cournot and Bertrand. (deposited 27 Dec 2016 18:58)
 Maximin and minimax strategies in symmetric multiplayers game with two strategic variables. (deposited 22 Jan 2017 14:48) [Currently Displayed]