Satoh, Atsuhiro and Tanaka, Yasuhito (2016): Two person zero-sum game with two sets of strategic variables.
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Abstract
We consider a two-person zero-sum 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 |
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Original Title: | Two person zero-sum game with two sets of strategic variables |
Language: | English |
Keywords: | zero-sum 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: | 73272 |
Depositing User: | Yasuhito Tanaka |
Date Deposited: | 26 Aug 2016 20:50 |
Last Modified: | 30 Sep 2019 17:43 |
References: | Kindler, J. (2005), ``A simple proof of Sion's minimax theorem'', American Mathematical Monthly, 112, pp. 356-358. Komiya, H. (1988), ``Elementary proof for Sion's minimax theorem'', Kodai Mathematical Journal, 11, pp. 5-7. Matsumura, T., Matsushima,N. and Cato,S. (2013), ``Competitiveness and R\&D competition revisited'' Economic Modelling, 31, 541-547. Satoh, A. and Tanaka, Y. (2013), ``Relative profit maximization and Bertrand equilibrium with quadratic cost functions'', Economics and Business Letters, 2, pp. 134-139. Satoh, A. and Tanaka, Y. (2014a), ``Relative profit maximization and equivalence of Cournot and Bertrand equilibria in asymmetric duopoly'', Economics Bulletin, 34, pp. 819-827. Satoh, A. and Tanaka, Y. (2014b), ``Relative profit maximization in asymmetric oligopoly'', Economics Bulletin, 34, 1653-1664. Sion, M. (1958), ``On general minimax theorems'', Pacific Journal of Mathematics, 8, pp. 171-176. ``Equivalence of Cournot and Bertrand equilibria in differentiated duopoly under relative profit maximization with linear demand'', Economics Bulletin, 33, 1479-1486. Tanaka, Y. (2013b), ``Irrelevance of the choice of strategic variables in duopoly under relative profit maximization'', Economics and Business Letters, 2, pp. 75-83. Vega-Redondo, F. (1997), ``The evolution of Walrasian behavior'' Econometrica 65, 375-384. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/73272 |
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