Stochastic Differential Games for Which the Open-Loop Equilibrium is Subgame Perfect
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It is generally admitted that a correct forecasting of uncertain variables needs Markov decision rules. In a dynamic game environment, this belief is reinforced if one focuses on credible actions of the players. Usually, subgame perfectness requires equilibrium strategies to be constructed on Markov rules. It comes as a surprise that there are interesting classes of stochastic differential games where the equilibrium based on open-loop strategies is subgame perfect. This fact is well known for deterministic games. We explore here the stochastic case, not dealt with up to now, identifying different game structures leading to the subgame perfectness of the open-loop equilibrium.
KeywordsStochastic differential game Open-loop strategies Feedback strategies Markov Perfect Nash Equilibrium
Mathematics Subject Classification49N70 49N90 91A23
We gratefully acknowledge the constructive comments of two anonymous referees and the associate editor. Support from the Ministerio de Economía y Competitividad (Spain), grants ECO 2014-56384-P, MDM 2014-0431, and Comunidad de Madrid, MadEco-CM S2015/HUM-3444 is gratefully acknowledged.