We define Player-Compatible Equilibrium or "PCE," which imposes cross-player restrictions on  magnitudes of the players' "trembles" onto different strategies. These restrictions are inspired by the idea that trembles correspond to deliberate experiments by inexperienced agents who are unsure of the prevailing distribution of play in opponent populations, and that different players' relative "compatibilities" with various strategies determine the relative frequencies of their experiments. We show that PCE selects the "intuitive " equilibria in a number of examples where trembling-hand perfect equilibrium (Selten, 1975) and proper equilibrium (Myerson, 1978) have no bite. We also provide learning-based microfoundations for our cross-player tremble restrictions in a class of games using three different specifications of how agents handle the exploration/exploitation trade-off: expected utility maximization, Bayesian upper confidence bounds, and Thompson sampling. Finally, we conduct a lab experiment based on one of our examples and verify PCE leads to better predictions than other equilibrium concepts .
 Player-Compatible Equilibrium (PCE) imposes cross-player restrictions on the magnitudes of the players' "trembles" onto different strategies. These restrictions capture the idea that trembles correspond to deliberate experiments by agents who are unsure of the prevailing distribution of play . PCE selects intuitive equilibria in a number of examples where trembling-hand perfect equilibrium (Selten, 1975) and proper equilibrium (Myerson, 1978) have no bite. We show that rational learning and some near-optimal heuristics imply our compatibility restrictions in a steady-state setting and verify that our theoretical predictions also apply to finite-population simulations when all agents start learning at the same time .
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also provide learning-based microfoundations for our cross-player tremble
show that rational learning and some near-optimal heuristics imply our compatibility
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class of games using three different specifications of how agents handle the exploration/exploitation trade-off: expected utility maximization, Bayesian upper confidence bounds, and Thompson sampling. Finally, we conduct a lab experiment based on one of our examples and verify PCE leads to better predictions than other equilibrium concepts
steady-state setting and verify that our theoretical predictions also apply to finite-population simulations when all agents start learning at the same time