A comparison of discrete fixed point theorems via a bimatrix game

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Abstract

There are three types of discrete fixed point theorems: type M and type C deal with monotone mappings and contraction mappings, respectively. Type B is based on Brouwer's fixed point theorem. The main aim of this paper is to compare type B with type M by applying them to a bimatrix game. For this purpose we characterize the direction preserving condition that is used in type B in terms of the best response mappings of the bimatrix game. Further we extend the characterization to a non-cooperative n-person game.

Original languageEnglish
Pages (from-to)1501-1510
Number of pages10
JournalJournal of Nonlinear and Convex Analysis
Volume16
Issue number8
Publication statusPublished - 2015

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology
  • Control and Optimization
  • Applied Mathematics

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