Tanaka, Yasuhito and Satoh, Atsuhiro (2017): Maximin and minimax strategies in twoplayers game with two strategic variables.
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Abstract
We examine maximin and minimax strategies for players in twoplayers game with two strategic variables and . We consider two patterns of game; one is the xgame in which strategic variables of players are x's, and the other is the pgame in which strategic variables of players are p's. We call two players Players A and B, and will show that the maximin strategy and the minimax strategy in the xgame, and the maximin strategy and the minimax strategy in the pgame are all equivalent for each player. However, the maximin strategy for Player A and that for Player B are not necessarily equivalent, and they 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 Player B is the opposite of the objective function of Player A, the maximin strategy for Player A and that for Player B are equivalent, and they constitute the Nash equilibrium both in the xgame and the pgame.
Item Type:  MPRA Paper 

Original Title:  Maximin and minimax strategies in twoplayers game with two strategic variables 
Language:  English 
Keywords:  twoplayers 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:  76352 
Depositing User:  Yasuhito Tanaka 
Date Deposited:  22 Jan 2017 14:40 
Last Modified:  26 Sep 2019 14:47 
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), ``Two person zerosum game with two sets of strategic variables'', MPRA Paper 73472, University Library of Munich, Germany. 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/76352 
Available Versions of this Item

Maximin and minimax strategies in asymmetric duopoly: Cournot and Bertrand. (deposited 23 Sep 2016 09:19)
 Maximin and minimax strategies in twoplayers game with two strategic variables. (deposited 22 Jan 2017 14:40) [Currently Displayed]