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

  • Tiziano De Angelis (a1) and Giorgio Ferrari (a2)

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.

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Corresponding author

* Postal address: School of Mathematics, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, UK. Email address: t.deangelis@leeds.ac.uk
** Postal address: Center for Mathematical Economics, Bielefeld University, Universitätsstrasse 25, D-33615 Bielefeld, Germany. Email address: giorgio.ferrari@uni-bielefeld.de

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Advances in Applied Probability
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