A penalty method approach for open-loop variational games with equality constraints

Abstract

In this paper we consider the possibility of solving a variational game with equality constraints by using a penalty method approach. Under the assumption that the unconstrained penalized games have open loop Nash equilibria we give conditions on our model to ensure that there exists a subsequence of penalty parameters converging to infinity for which the corresponding sequence of solutions to the penalized games converges to an open loop Nash equilibrium of the constrained game. Our conditions are based on classical growth and convexity conditions found in the calculus of variations. We conclude our paper with some remarks on obtaining the solutions of the penalized games via Leitmann’s direct method.