Evolution of noisy learning in games

TL;DR

This paper investigates how strategies and sensitivities co-evolve in game-theoretic learning, revealing that the evolution of noisy learning depends on the game type and can lead to various stable or branching behaviors.

Contribution

It introduces a co-evolutionary framework for strategies and sensitivities, showing how different game types influence the evolution of learning noise and sensitivity levels.

Findings

Sensitivities often increase indefinitely in prisoner's dilemmas.

In snowdrift and stag-hunt games, sensitivities tend to stabilize or branch.

Noisy learning can be an adaptive feature, not just a cognitive limitation.

Abstract

People make strategic decisions many times a day - during negotiations, when coordinating actions with others, or when choosing partners for cooperation. The resulting dynamics can be studied with learning theory and evolutionary game theory. These frameworks explore how people adapt their decisions over time, in light of how effective their strategies have been. The outcomes of such learning processes depend on how sensitive individuals are to the performance of their strategies. When they are more sensitive, they systematically favor strategies they deem more successful. When they are less sensitive, their learning process is noisier and more erratic. Traditionally, most models treat this sensitivity as a fixed parameter - like the "selection strength" parameter in evolutionary models. Instead, we study how strategies and sensitivities co-evolve. We find that the co-evolutionary endpoints depend on both the type of strategic interaction and the learning rule employed. In prisoner's dilemmas, we often observe sensitivities to increase indefinitely. But in snowdrift and stag-hunt games, sensitivities often converge to a finite value, or we observe evolutionary branching altogether. These results shed light on how evolution might shape learning mechanisms for social behavior. They suggest that noisy learning does not need to be a by-product of cognitive constraints. Instead, it can serve as a means to gain strategic advantages.