Reinforcement learning in signaling game

TL;DR

This paper extends the analysis of a signaling game to more general settings, proving convergence of expected payoff and characterizing the structure of limit configurations in complex signaling scenarios.

Contribution

It generalizes previous models by analyzing signaling games with arbitrary numbers of states, signals, and acts, establishing convergence and structural properties of the resulting communication patterns.

Findings

Expected payoff converges almost surely.

A limit bipartite graph with no synonym or bottleneck emerges.

Any such graph can be a limit configuration with positive probability.

Abstract

We consider a signaling game originally introduced by Skyrms, which models how two interacting players learn to signal each other and thus create a common language. The first rigorous analysis was done by Argiento, Pemantle, Skyrms and Volkov (2009) with 2 states, 2 signals and 2 acts. We study the case of M_1 states, M_2 signals and M_1 acts for general M_1, M_2. We prove that the expected payoff increases in average and thus converges a.s., and that a limit bipartite graph emerges, such that no signal-state correspondence is associated to both a synonym and an informational bottleneck. Finally, we show that any graph correspondence with the above property is a limit configuration with positive probability.