Finding normalized equilibrium in convex-concave games

S. D. Flm, A. Ruszczyński

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This paper considers a fairly large class of noncooperative games in which strategies are jointly constrained. When what is called the Ky Fan or Nikaidô-Isoda function is convex-concave, selected Nash equilibria correspond to diagonal saddle points of that function. This feature is exploited to design computational algorithms for finding such equilibria. To comply with some freedom of individual choice the algorithms developed here are fairly decentralized. However, since coupling constraints must be enforced, repeated coordination is needed while underway towards equilibrium. Particular instances include zero-sum, two-person games - or minimax problems - that are convex-concave and involve convex coupling constraints.

Original languageEnglish (US)
Pages (from-to)37-51
Number of pages15
JournalInternational Game Theory Review
Issue number1
StatePublished - Mar 2008

All Science Journal Classification (ASJC) codes

  • Business and International Management
  • Computer Science(all)
  • Statistics, Probability and Uncertainty


  • Exact penalty
  • Joint constraints
  • Ky Fan or Nikaidô-Isoda functions
  • Nash equilibrium
  • Noncooperative games
  • Partial regularization
  • Proximal point algorithm
  • Quasi-variational inequalities
  • Saddle points
  • Subgradient projection


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