A Martingale Theory for a Class of Dynkin Games with Asymmetric Information

In this thesis we study a class of Dynkin games with asymmetric information where players’ strategies are randomised stopping times. Information asymmetry is formulated as an exogenous random variable taking finitely many values, the outcome of which is only known by the minimiser. It is already known that for these types of games there exists both a value and a Nash equilibrium, however, these results are non-constructive and as such they provide no information regarding the properties of the value or the optimal strategies of the players.

Inspired by our additional work on classical results for games with full information, we introduce a martingale theory to derive a set of necessary and sufficient conditions for the existence of a value and a Nash equilibrium, characterising the game. By defining three processes—a martingale, a submartingale and a supermartingale—we are also able to characterise the optimal strategies of both players and their optimal subgame strategies. We finish this work with an example in which we use our necessary conditions to deduce the form of the optimal strategies, and then verify them to be optimal using our sufficient conditions.