# Learning and Type Compatibility in Signaling Games

## TL;DR

This paper develops a learning-based model for signaling games, explaining how off-path beliefs and equilibrium outcomes depend on sender experiments and type compatibility, using Gittins index to predict behavior.

## Contribution

It introduces a micro-foundation for off-path beliefs in signaling games through non-equilibrium learning, linking sender experimentation to equilibrium selection via type compatibility.

## Key findings

- Different sender types experiment differently based on payoffs.
- Off-path beliefs are constrained by type compatibility.
- The Gittins index predicts sender signaling behavior.

## Abstract

Which equilibria will arise in signaling games depends on how the receiver interprets deviations from the path of play. We develop a micro-foundation for these off-path beliefs, and an associated equilibrium refinement, in a model where equilibrium arises through non-equilibrium learning by populations of patient and long-lived senders and receivers. In our model, young senders are uncertain about the prevailing distribution of play, so they rationally send out-of-equilibrium signals as experiments to learn about the behavior of the population of receivers. Differences in the payoff functions of the types of senders generate different incentives for these experiments. Using the Gittins index (Gittins, 1979), we characterize which sender types use each signal more often, leading to a constraint on the receiver's off-path beliefs based on "type compatibility" and hence a learning-based equilibrium selection.