Towards a taxonomy of learning dynamics in 2 × 2 games

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 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.Marco Pangallo performed the research presented in this paper when he was affiliated to the Institute for New Economic Thinking and Mathematical Institute at the University of Oxford. He acknowledges financial support from INET and from the EPSRC award number 1657725. Tobias Galla acknowledges financial support from the Agencia Estatal de Investigacion (AEI, MCI, Spain) and Fondo Europeo de Desarrollo Regional (FEDER, UE) under Project PACSS (RTI2018-093732-B-C21/C22), and the Maria de Maeztu Program for units of Excellence in R&D, grant MDM-2017-0711 funded by MCIN/AEI/10.13039/501100011033. Doyne Farmer acknowledges financial support from Baillie Gifford