Learning by Imitation in Games: Theory, Field, and Laboratory∗

We exploit a unique opportunity to study how a large population of players in the field learn to play a novel game with a complicated and non-intuitive mixed strategy equilibrium. We argue that standard models of belief-based learning and reinforcement learning are unable to explain the data, but that a simple model of similarity-based global cumulative imitation can do so. We corroborate our findings using laboratory data from a scaled-down version of the same game, and demonstrate out-of-sample explanatory power in three other games. The theoretical properties of the proposed learning model are studied by means of stochastic approximation. jel classification: C72, C73, L83. keywords: Learning; imitation; behavioral game theory; evolutionary game theory; stochastic approximation; replicator dynamic; similarity-based reasoning; generalization; mixed equilibrium. ∗We are grateful for comments from Ingela Alger, Alan Beggs, Ken Binmore, Colin Camerer, Vincent Crawford, Ido Erev, David Gill, Yuval Heller, and Peyton Young, as well as seminar audiences at the Universities of Edinburgh, Essex, Lund, Oxford, Warwick and St Andrews, University College London, the 4th World Congress of the Game Theory Society in Istanbul, the 67th European Meeting of the Econometric Society, and the 8th Nordic Conference on Behavioral and Experimental Economics. Kristaps Dzonsons (k -Consulting) and Kaidi Sun provided excellent research assistance. Erik Mohlin acknowledges financial support from the European Research Council, Grant no. 230251, Robert Östling acknowledges financial support from the Jan Wallander and Tom Hedelius Foundation, and Joseph Tao-yi Wang acknowledges support from the NSC of Taiwan. †Nuffi eld College and Department of Economics, University of Oxford. Address: Nuffi eld College, New Road, Oxford OX1 4PX, United Kingdom. E-mail: erik.mohlin@nuffi eld.ox.ac.uk. ‡Institute for International Economic Studies, Stockholm University, SE—106 91 Stockholm, Sweden. E-mail: [email protected]. §Department of Economics, National Taiwan University, 21 Hsu-Chow Road, Taipei 100, Taiwan. E-mail: [email protected].