Player-Compatible Learning and Player-Compatible Equilibrium

TL;DR

Player-Compatible Equilibrium (PCE) introduces cross-player tremble restrictions reflecting deliberate experimentation, selecting intuitive equilibria where traditional concepts like trembling-hand perfect and proper equilibria fail, with implications for rational learning.

Contribution

The paper proposes Player-Compatible Equilibrium, a novel equilibrium concept incorporating cross-player tremble restrictions, and links it to rational learning and fictitious play.

Findings

PCE captures intuitive equilibria missed by traditional refinements.

Steady-state rational learning supports PCE compatibility restrictions.

PCE outperforms trembling-hand and proper equilibria in certain examples.

Abstract

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 weighted fictitious play imply our compatibility restrictions in a steady-state setting.