Structures of Stochastic Differential Games for Which the Open-Loop Equilibrium Is Subgame Perfect

Abstract

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 focus on credible actions of the players. Usually, subgame perfectness requires equilibrium strategies being 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.