FINDING NORMALIZED EQUILIBRIUM IN CONVEX-CONCAVE GAMES

S. D. Flåm () and Andrzej Ruszczynski ()
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S. D. Flåm: Economics Department, Bergen University, 5007 Bergen, Norway

International Game Theory Review (IGTR), 2008, vol. 10, issue 01, 37-51

Abstract: 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.

Keywords: Noncooperative games; Nash equilibrium; joint constraints; quasi-variational inequalities; exact penalty; subgradient projection; proximal point algorithm; partial regularization; saddle points; Ky Fan or Nikaidô-Isoda functions; Subject Classification: 90C25; Subject Classification: 91A10 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S0219198908001765

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