# Towards a taxonomy of learning dynamics in 2 x 2 games

## TL;DR

This paper provides a comprehensive analysis of Experience-Weighted Attraction (EWA) in 2x2 games, revealing its convergence properties and dynamic behaviors, including new insights into equilibrium selection and complex dynamics.

## Contribution

It offers a unified framework for understanding learning dynamics in 2x2 games by analyzing EWA, encompassing and extending previous learning models with novel results.

## Key findings

- EWA converges only to Pareto-efficient equilibria in coordination games.
- EWA can lead to convergence to mutual cooperation in Prisoner Dilemmas.
- Longer or shorter memory influences the likelihood of cycles or chaos.

## Abstract

Do boundedly rational players learn to choose equilibrium strategies as they play a game repeatedly? A large literature in behavioral game theory has proposed and experimentally tested various learning algorithms, but a comparative analysis of their equilibrium convergence properties is lacking. In this paper we analyze Experience-Weighted Attraction (EWA), which generalizes fictitious play, best-response dynamics, reinforcement learning and also replicator dynamics. Studying $2\times 2$ games for tractability, we recover some well-known results in the limiting cases in which EWA reduces to the learning rules that it generalizes, but also obtain new results for other parameterizations. For example, we show that in coordination games EWA may only converge to the Pareto-efficient equilibrium, never reaching the Pareto-inefficient one; that in Prisoner Dilemma games it may converge to fixed points of mutual cooperation; and that limit cycles or chaotic dynamics may be more likely with longer or shorter memory of previous play.