Finding Normalized Equilibrium in Convex-Concave Games
International Game Theory Review, Vol. 10, No 1, pp. 37-51, 2008
Posted: 29 Oct 2009
Date Written: March 2008
Abstract
This paper considers a fairly large class of non-cooperative 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 mini-max problems - that are convex-concave and involve convex coupling constraints.
Keywords: Non-cooperative 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
Suggested Citation: Suggested Citation