A Class of Stochastic Games and Moving Free Boundary Problems

X. Guo, W. Tang, R. Xu, “A class of stochastic games and moving free boundary problems”. SIAM Journal on Control and Optimization 60 (2), 758-785

Abstract. In this paper we propose and analyze a class of 𝑁-player stochastic games that include finite fuel stochastic games as a special case. We first derive sufficient conditions for the Nash equilibrium (NE) in the form of a verification theorem. The associated quasi-variational-inequalities include an essential game component regarding the interactions among players, which may be interpreted as the analytical representation of the conditional optimality for NEs. The derivation of NEs involves solving first a multidimensional free boundary problem and then a Skorokhod problem. Finally, we present an intriguing connection between these NE strategies and controlled rank-dependent stochastic differential equations.