Satoh, Atsuhiro and Tanaka, Yasuhito
(2016):
*Symmetric multi-person zero-sum game with two sets of strategic variables.*

Preview |
PDF
MPRA_paper_75838.pdf Download (77kB) | Preview |

## Abstract

We consider a symmetric multi-person zero-sum game with two sets of alternative strategic variables which are related by invertible functions. They are denoted by (s1, s2, ..., sn) and (t1, t2, ..., tn) for players 1, 2, ..., n. The number of players is larger than two. We consider a symmetric game in the sense that all players have the same payoff functions. We do not postulate differentiability of the payoff functions of players. We will show that the following patterns of competition, 1) all players choose si, 2) all players choose ti and 3) m players choose ti, i=1, ..., m and n-m players choose sj, j=m+1, ..., n where 1<=m<=n-1, are equivalent, that is, they yield the same outcome. However, in an asymmetric zero-sum game with more than two players the equivalence does not hold.

Item Type: | MPRA Paper |
---|---|

Original Title: | Symmetric multi-person zero-sum game with two sets of strategic variables |

Language: | English |

Keywords: | multi-person zero-sum game, two strategic variables |

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: | 75838 |

Depositing User: | Yasuhito Tanaka |

Date Deposited: | 01 Aug 2017 05:19 |

Last Modified: | 13 Oct 2019 04:54 |

References: | Glicksberg, I.L. (1952), ``A further generalization of the Kakutani fixed point theorem,'' Proceedings of the American Mathematical Society, 3, 170–174. Matsumura, T., N. Matsushima and S. Cato (2013) ``Competitiveness and R&D competition revisited'' Economic Modelling, 31, 541-547. Satoh, A. and Y. Tanaka (2013) ``Relative profit maximization and Bertrand equilibrium with quadratic cost functions,'' Economics and Business Letters, 2, pp. 134-139, 2013. Satoh, A. and Y. Tanaka (2014a) ``Relative profit maximization and equivalence of Cournot and Bertrand equilibria in asymmetric duopoly,'' Economics Bulletin, 34, pp. 819-827, 2014. Satoh, A. and Y. Tanaka (2014b), ``Relative profit maximization in asymmetric oligopoly,'' Economics Bulletin, 34, 1653-1664. Satoh, A. and Tanaka, Y. (2016), ``Maximin and minimax strategies in symmetric oligopoly,'' mimeo. Tanaka, Y. (2013a) ``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, 2013. Vega-Redondo, F. (1997) ``The evolution of Walrasian behavior'' Econometrica 65, 375–-384. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/75838 |