Stochastic nonzero-sum games: a new connection between singular control and optimal stopping

Abstract

de Angelis T, Ferrari G. Stochastic nonzero-sum games: a new connection between singular control and optimal stopping . Center for Mathematical Economics Working Papers. Vol 565. Bielefeld: Center for Mathematical Economics; 2016.In this paper we establish a new connection between a class of 2-player nonzerosum games of optimal stopping and certain 2-player nonzero-sum games of singular control. We show that whenever a Nash equilibrium in the game of stopping is attained by hitting times at two separate boundaries, then such boundaries also trigger a Nash equilibrium in the game of singular control. Moreover a differential link between the players' value functions holds across the two games