Strong randomized mean-field equilibria exist for optimal-stopping games with countably generated common noise under continuity assumptions, and monotone comparative statics hold for strict equilibria.
Bertucci, Optimal stopping in mean field games, an obstacle problem approach
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Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noise
Strong randomized mean-field equilibria exist for optimal-stopping games with countably generated common noise under continuity assumptions, and monotone comparative statics hold for strict equilibria.