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Nash equilibria for nonzero-sum ergodic stochastic differential games

Part of: Miscellaneous topics in calculus of variations and optimal control Stochastic systems and control Game theory

Published online by Cambridge University Press:  30 November 2017

Samuel N. Cohen  and
Victor Fedyashov
Samuel N. Cohen*
Affiliation:
University of Oxford
Victor Fedyashov*
Affiliation:
University of Oxford
*
* Postal address: Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK.
* Postal address: Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK.
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Abstract

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We consider nonzero-sum games where multiple players control the drift of a process, and their payoffs depend on its ergodic behaviour. We establish their connection with systems of ergodic backward stochastic differential equations, and prove the existence of a Nash equilibrium under generalised Isaac's conditions. We also study the case of interacting players of different type.

Keywords

Ergodic gameNash equilibriumBSDE

MSC classification

Primary: 91A60: Probabilistic games; gambling
Secondary: 49N70: Differential games 93E20: Optimal stochastic control
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 4 , December 2017 , pp. 977 - 994
Copyright
Copyright © Applied Probability Trust 2017 

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