A biconvex optimization problem to compute Nash equilibrium in nplayer games and an algorithm
Abstract
In this paper we present optimization problems with biconvex objective function and linear constraints such that the set of global minima of the optimization problems is the same as the set of Nash equilibria of a nplayer generalsum normal form game. We further show that the objective function is an invex function and consider a projected gradient descent algorithm. We prove that the projected gradient descent scheme converges to a partial optimum of the objective function. We also present simulation results on certain test cases showing convergence to a Nash equilibrium strategy.
 Publication:

arXiv eprints
 Pub Date:
 April 2015
 arXiv:
 arXiv:1504.06828
 Bibcode:
 2015arXiv150406828Y
 Keywords:

 Computer Science  Computer Science and Game Theory