The method of analytic centers knownin convex programming is implemented for the construction of paths leading to equilibrium points in mixed strategy bimatrix games.A bimatrix game is extended to a family of time-parametrized perturbed games in which the payofs are logarithmically penalized for the approach to the boundary of the strategy space.In the interior of the strategy space the penalties' relative weights vanish as time goes to infinity.It is shown that the Nash equilibria in the perturbed games converge to those in the unperturbed game.Moreover,equilibrium paths starting in a connected set converge to a same equilibrium,and,under appropriate nondegeneracy conditions,"almost all" equilibrium paths converge to a single interior equilibrium.
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