Payoff Information and Learning in Signaling Games

Abstract

We add the assumption that players know their opponents' payoff functions and rationality to a model of non-equilibrium learning in signaling games. Agents are born into player roles and play against random opponents every period. Inexperienced agents are uncertain about the prevailing distribution of opponents' play, but believe that opponents never choose conditionally dominated strategies. Agents engage in active learning and update beliefs based on personal observations. Payoff information can refine or expand learning predictions, since patient young senders' experimentation incentives depend on which receiver responses they deem plausible. We show that with payoff knowledge, the limiting set of long-run learning outcomes is bounded above by rationality-compatible equilibria (RCE), and bounded below by uniform RCE. RCE refine the Intuitive Criterion (Cho and Kreps, 1987) and include all divine equilibria (Banks and Sobel, 1987). Uniform RCE sometimes but not always exists, and implies universally divine equilibrium.Comment: This material was previously part of a larger paper titled "Type-Compatible Equilibria in Signalling Games," which split into two smaller papers: "Learning and Type Compatibility in Signaling Games" and "Payoff Information and Learning in Signaling Games.