Reversibility and oscillations in zero-sum discounted stochastic games

Sylvain  Sorin; Guillaume  Vigeral

doi:10.3934/jdg.2015.2.103

Article Contents

2015, Volume 2, Issue 1: 103-115. Doi: 10.3934/jdg.2015.2.103

This issue Previous Article Discrete time mean field games: The short-stage limit Next Article

Reversibility and oscillations in zero-sum discounted stochastic games

Sylvain Sorin^1, and
Guillaume Vigeral^2,

1.
Sorbonne Universités, UPMC Univ Paris 06, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Univ Paris Diderot, Sorbonne Paris Cité, F-75005, Paris
2.
Université Paris-Dauphine, CEREMADE, Place du Maréchal De Lattre de Tassigny, 75775 Paris cedex 16

Received: October 31, 2014

Revised: December 31, 2014

Published: December 2014

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Abstract

We show that by coupling two well-behaved exit-time problems one can construct two-person zero-sum dynamic games having oscillating discounted values. This unifies and generalizes recent examples of stochastic games with finite state space, due to Vigeral (2013) and Ziliotto (2013).

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Mathematics Subject Classification: Primary: 91A15, 91A05; Secondary: 91A25.

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References

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