Scandinavian Working Papers in Economics

Working Papers in Economics,
University of Bergen, Department of Economics

No 05/06: Computing Normalized Equilibria in Convex-Concave Games

Sjur Didrik Flåm () and A. Ruszczynski ()
Additional contact information
Sjur Didrik Flåm: University of Bergen, Department of Economics, Postal: Hermann Fossgt. 6, N-5007 Bergen, Norway
A. Ruszczynski: Rutgers University, Department of Management Science and Information Systems

Abstract: 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; quasivariational inequalities; exact penalty; subgradient projection; proximal point algorithm; partial regularization; saddle points; Ky Fan or Nikaidô-Isoda functions.

JEL-codes: C63; C70

15 pages, April 26, 2006

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