Robust nash equilibria in N-person non-cooperative games: Uniqueness and reformulation

Ryoichi Nishimura, Shunsuke Hayashi, Masao Fukushima

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

In this paper we propose a general framework of distribution-free models for N-person noncooperative games with uncertain information. In the model, we assume that each player's cost function and/or the opponents' strategies belong to some uncertainty sets, and each player chooses his/her strategy according to the robust optimization policy. Under such assumptions, we define the robust Nash equilibrium for N-person games by extending some existing definitions. We present sufficient conditions for existence and uniqueness of a robust Nash equilibrium. In order to compute robust Nash equilibria, we reformulate certain classes of robust Nash equilibrium problems to second-order cone complementarity problems. We finally show some numerical results to discuss the behavior of robust Nash equilibria.

Original languageEnglish
Pages (from-to)237-259
Number of pages23
JournalPacific Journal of Optimization
Volume5
Issue number2
Publication statusPublished - 2009 May 1
Externally publishedYes

Keywords

  • Complementarity problem
  • Incomplete information
  • N-person non-cooperative game
  • Robust Nash equilibrium
  • Robust optimization

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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