Stochastic nonzero-sum games: A new connection between singular control and optimal stopping - Tiziano De Angelis; Giorgio Ferrari (Bielefeld University, Center for Mathematical Economics (IMW), 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.
urn:nbn:de:0070-pub-29047538
Keywords: 330; games of singular control; games of optimal stopping; Nash equilibrium; onedimensional diffusion; Hamilton-Jacobi-Bellman equation; verification theorem