Satoh, Atsuhiro and Tanaka, Yasuhito (2016): Maximin and minimax strategies in symmetric oligopoly: Cournot and Bertrand.
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Abstract
We examine maximin and minimax strategies for firms under symmetric oligopoly 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 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 for the firms are all equivalent. However, the maximin strategy for the firms 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 one firm is the opposite of the sum of the objective functions of other firms, the maximin and the minimax strategies for the firms constitute the Nash equilibrium both in the Cournot game and the Bertrand game.
Item Type:  MPRA Paper 

Original Title:  Maximin and minimax strategies in symmetric oligopoly: Cournot and Bertrand 
Language:  English 
Keywords:  maximin strategy, minimax strategy, oligopoly 
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:  75837 
Depositing User:  Yasuhito Tanaka 
Date Deposited:  27 Dec 2016 18:58 
Last Modified:  29 Sep 2019 03:00 
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/75837 
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