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A pathwise approach to Dynkin games

We reduce the classical discrete-time game of optimal stopping between two players, known as "Dynkin game", to a pathwise (deterministic) game of timing, by addition of a suitable non-adapted compensator (λ n ) to the payoff. This compensator satisfies iB(λ n |^ 7 n ) = 0, where T n is the information available to the players at time t = n, and IE de-notes expectation with respect to the underlying probability measure IP; the compensator also enforces the non-anticipatiυity constraint that the strategies of both players be stopping times of (^>ι) A pair of such stopping times is identified, which leads to a saddle-point for each of these games; and it is shown that the value V of the stochastic game is obtained by "averaging out" the value W(ω) of the pathwise game: V = J n W(ω)P(dω).