Tanaka, Yasuhito and Satoh, Atsuhiro (2016): Maximin and minimax strategies in asymmetric duopoly: Cournot and Bertrand.
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Abstract
We examine maximin and minimax strategies for firms in asymmetric duopoly with differentiated goods. We consider two patterns of game; the Cournot game in which strategic variables of the firms are their outputs, and the Bertrand game in which strategic variables of the firms are the prices of their goods. We call two firms Firm A and B, and will show that the maximin strategy and the minimax strategy in the Cournot game, and the maximin strategy and the minimax strategy in the Bertrand game are all equivalent for each firm. However, the maximin strategy (or the minimax strategy) for Firm A and that for Firm B are not necessarily equivalent, and they are not necessarily equivalent to their Nash equilibrium strategies in the Cournot game nor the Bertrand game.. But, in a special case, where the objective function of Firm B is the opposite of the objective function of Firm A, the maximin strategy for Firm A and that for Firm B are equivalent, and they constitute the Nash equilibrium both in the Cournot game and the Bertrand game. This special case corresponds to relative profit maximization by the firms.
Item Type:  MPRA Paper 

Original Title:  Maximin and minimax strategies in asymmetric duopoly: Cournot and Bertrand 
Language:  English 
Keywords:  maximin strategy, minimax strategy, duopoly 
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:  73925 
Depositing User:  Yasuhito Tanaka 
Date Deposited:  23 Sep 2016 09:19 
Last Modified:  30 Sep 2019 21:55 
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/73925 
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