ABSTRACT
The method of analytic centers known in convex programming is implemented for 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 payoffs are logarithmically penalized for the approach to the boundary of the strategy space. Homotopy, or path following, optimization methods rest on the idea of approaching an optimum along the family of solutions of time-parametrized perturbed optimization problems. The initial perturbed problem is normally chosen simple enough so that the initial point on a solution path is easily identified, and the final problem is the unperturbed one. In a general path following methodology for finding equilibria — without a detailed analysis of the existence of the solution paths — was presented. In a homotopy method was in the base of a proof of the oddness of the number of equilibrium points in a bimatrix game.
