Satoh, Atsuhiro and Tanaka, Yasuhito (2016): Two person zerosum game with two sets of strategic variables.
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Abstract
We consider a twoperson zerosum game with two sets of strategic variables which are related by invertible functions. They are denoted by (sA, sB) and (tA, tB) for players A and B.
We will show that the following four patterns of competition are equivalent, that is, they yield the same outcome.
1. Player A and B choose sA and sB (competition by (sA, sB)).
2. Player A and B choose tA and tB (competition by (tA, tB)).
3. Player A and B choose tA and sB (competition by (tA, sB)).
4. Player A and B choose sA and tB (competition by (sA, tB)).
Item Type:  MPRA Paper 

Original Title:  Two person zerosum game with two sets of strategic variables 
Language:  English 
Keywords:  zerosum game, two strategic variables, equivalence of outcome 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games L  Industrial Organization > L1  Market Structure, Firm Strategy, and Market Performance > L13  Oligopoly and Other Imperfect Markets 
Item ID:  73704 
Depositing User:  Yasuhito Tanaka 
Date Deposited:  17 Sep 2016 10:39 
Last Modified:  17 Sep 2016 10:41 
References:  Kindler, J. (2005), ``A simple proof of Sion's minimax theorem'', American Mathematical Monthly, 112, pp. 356358. Komiya, H. (1988), ``Elementary proof for Sion's minimax theorem'', Kodai Mathematical Journal, 11, pp. 57. 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. Sion, M. (1958), ``On general minimax theorems'', Pacific Journal of Mathematics, 8, pp. 171176. ``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/73704 
Available Versions of this Item

Two person zerosum game with two sets of strategic variables. (deposited 26 Aug 2016 20:50)

Two person zerosum game with two sets of strategic variables. (deposited 03 Sep 2016 15:54)
 Two person zerosum game with two sets of strategic variables. (deposited 17 Sep 2016 10:39) [Currently Displayed]

Two person zerosum game with two sets of strategic variables. (deposited 03 Sep 2016 15:54)