Robust Sequential Stopping Games

We study the robust equilibrium for sequential stopping games to give the conditions under which the game’s values exist. Three scenarios of the game are analyzed. G 1 is the game where only the maximizing player optimizes in a worst-case scenario and G 2 is the game where only the minimizing player optimizes in a worst-case scenario.We show that under the conditions of integrability and time consistency, the game value exists for robust zero-sum two-person sequential stopping games ( G 1 , G 2 ) when the payoff process is an ambiguous adapted process under multiple probability measures. We also establish the relationship between G 1 and G 2 . MSC Classification: 62L15 , 91A15