Martingale theory for Dynkin games with asymmetric information

This paper provides necessary and sufficient conditions for a pair of randomised stopping times to form a saddle point of a zero-sum Dynkin game with partial and/or asymmetric information across players. The framework is non-Markovian and covers essentially any information structure. Our methodology relies on the identification of suitable super and submartingales involving players’ equilibrium payoffs. Saddle point strategies are characterised in terms of the dynamics of those equilibrium payoffs and are related to their Doob-Meyer decompositions.