A Taxonomy of Learning Dynamics in 2 × 2 Games

35 Pages Posted: 8 Feb 2017 Last revised: 6 Apr 2020

See all articles by Marco Pangallo

Marco Pangallo

Scuola Superiore Sant'Anna di Pisa

James Sanders

University of Manchester

Tobias Galla

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: April 4, 2020

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 reply dynamics, reinforcement learning and also replicator dynamics. We provide a comprehensive analytical characterization of the asymptotic behavior of EWA learning in 2x2 games. 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 in Matching Pennies games it may fail to converge to any fixed point, following instead limit cycles or chaos.

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, A Taxonomy of Learning Dynamics in 2 × 2 Games (April 4, 2020). Available at SSRN: https://ssrn.com/abstract=2913183 or http://dx.doi.org/10.2139/ssrn.2913183

Marco Pangallo (Contact Author)

Scuola Superiore Sant'Anna di Pisa ( email )

Biblioteca Scuola Superiore Sant'Anna
Piazza Martiri della Liberta, n. 33
Pisa, 56127
Italy

James Sanders

University of Manchester ( email )

Oxford Road
Manchester, M13 9PL
United Kingdom

Tobias Galla

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 )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

HOME PAGE: http://www.inet.ox.ac.uk/people/view/4

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States
505-984-8800 (Phone)
505-982-0565 (Fax)

HOME PAGE: http://www.santafe.edu/~jdf/

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