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Non-Zero-Sum Stopping Games in Continuous Time

We consider a two-player non-zero-sum stopping game in which the payoff of each player is revealed when both players stop, instead of it being revealed after the first player's stopping time. Such problems appear in the context of economics and finance, e.g., when two company try to choose good times to enter or leave the market, or when two investors try to maximize their own utilities in the case that each player sells one American option to the other.