Towards a Taxonomy of Learning Dynamics in 2 × 2 Games

34 Pages Posted: 8 Feb 2017 Last revised: 2 Sep 2021

See all articles by Marco Pangallo

Marco Pangallo

CENTAI Institute

James Sanders

The University of Manchester

Tobias Galla

The University of Manchester - School of Physics and Astronomy

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; Santa Fe Institute

Date Written: September 2, 2021

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.

Keywords: Behavioural Game Theory, EWA Learning, Convergence, Equilibrium, Chaos

JEL Classification: C62, C73, D83

Suggested Citation

Pangallo, Marco and Sanders, James and Galla, Tobias and Farmer, J. Doyne, Towards a Taxonomy of Learning Dynamics in 2 × 2 Games (September 2, 2021). Available at SSRN: https://ssrn.com/abstract=2913183 or http://dx.doi.org/10.2139/ssrn.2913183

Marco Pangallo (Contact Author)

CENTAI Institute ( email )

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Italy

James Sanders

The University of Manchester ( email )

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Manchester, N/A M13 9PL
United Kingdom

Tobias Galla

The University of Manchester - School of Physics and Astronomy ( email )

United Kingdom

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

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Oxford, OX2 6ED
United Kingdom

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