Sjur Flam () and A. Ruszczynski ()
Sjur Flam: Economics Department, Bergen University, Postal: Economics Department, Bergen University , 5007 Bergen, Norway
A. Ruszczynski: Rutgers University, Department of Management Science and Information Systems, Postal: Department of Management Science and Information Systems,, Rutgers University
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 Nikaido-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 Nikaido-Isoda functions
15 pages, April 27, 2006
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