Satoh, Atsuhiro and Tanaka, Yasuhito (2016): Symmetric multiperson zerosum game with two sets of strategic variables.

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Abstract
We consider a symmetric multiperson zerosum 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 nm players choose sj, j=m+1, ..., n where 1<=m<=n1, are equivalent, that is, they yield the same outcome. However, in an asymmetric zerosum game with more than two players the equivalence does not hold.
Item Type:  MPRA Paper 

Original Title:  Symmetric multiperson zerosum game with two sets of strategic variables 
Language:  English 
Keywords:  multiperson zerosum 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 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/75838 