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

Tiziano De Angelis · Giorgio Ferrari

33 citations0/0 files storedAdvances in Applied Probability

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Stochastic processes and financial applications Game Theory and Applications Adaptive Dynamic Programming Control

Abstract

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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1994Investment Under Uncertainty.1994Investment under Uncertainty 2007Brownian Motion and Stochastic Calculus 2005Stochastic Integration and Differential Equations 2002Handbook of Brownian Motion - Facts and Formulae 2001Markov Perfect Equilibrium 1979Stochastic differential equations with reflecting boundary condition in convex regions 1992International aspects of pollution control

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