Payoff Information and Learning in Signaling Games

TL;DR

This paper explores how players' knowledge of opponents' payoffs influences learning outcomes in signaling games, showing that payoff information bounds long-run equilibria within rationality-compatible and uniform RCEs.

Contribution

It introduces a model where payoff knowledge affects active learning and characterizes the resulting set of long-run outcomes using refined equilibrium concepts.

Findings

Payoff information refines learning predictions.

Long-run outcomes are bounded by RCE and uniform RCE.

Uniform RCE may or may not exist, affecting equilibrium predictions.

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.