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In this paper we present optimization problems with biconvex objectivefunction and linear constraints such that the set of global minima of theoptimization problems is the same as the set of Nash equilibria of a n-playergeneral-sum normal form game. We further show that the objective function is aninvex function and consider a projected gradient descent algorithm. We provethat the projected gradient descent scheme converges to a partial optimum ofthe objective function. We also present simulation results on certain testcases showing convergence to a Nash equilibrium strategy.

A bi-convex optimization problem to compute Nash equilibrium in n-player games and an algorithm