Player-Compatible Equilibrium∗

We define Player-Compatible Equilibrium or “PCE,” which imposes cross-player restrictions on magnitudes of the players’ “trembles” onto different actions. These restrictions are inspired by the idea that trembles correspond to deliberate experiments by inexperienced agents who are unsure of the prevailing distribution of strategies in opponent populations. 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 a learning-based microfoundation for PCE in some easy-to-analyze classes of games. Finally, we conduct a lab experiment based on one of our examples and verify PCE leads to better predictions than other equilibrium concepts. ∗We thank Dave Rand for useful conversations and comments. We are grateful to the staff and research assistants at Harvard Decision Science Laboratory, especially Alki Iliopoulou, Gabe Mansur, Christina Qiu, and Sylvie Stoloff. We thank National Science Foundation grant SES 1643517 for financial support. †Department of Economics, MIT. Email: [email protected] ‡Department of Economics, Harvard University. Email: [email protected]