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

Published online by Cambridge University Press:  26 July 2018

Tiziano De Angelis
Affiliation:
University of Leeds
Giorgio Ferrari
Affiliation:
Bielefeld University

Abstract

In this paper we establish a new connection between a class of two-player nonzero-sum games of optimal stopping and certain two-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.

Type
Original Article
Copyright
Copyright © Applied Probability Trust 2018 

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