Cycles and Instability in a Rock-Paper-Scissors Population Game: A Continuous Time Experiment

Abstract

Cycles and Instability in a Rock-Paper-Scissors Population Game: a Continuous Time Experiment ∗ Timothy N. Cason † Daniel Friedman ‡ Ed Hopkins § Purdue University UC Santa Cruz University of Edinburgh July 19, 2012 Abstract We report laboratory experiments that use new, visually oriented software to ex- plore the dynamics of 3 × 3 games with intransitive best responses. Each moment, each player is matched against the entire population, here 8 human subjects. A “heat map” offers instantaneous feedback on current profit opportunities. In the continuous slow adjustment treatment, we see distinct cycles in the population mix. The cycle amplitude, frequency and direction are consistent with standard learning models. Cy- cles are more erratic and higher frequency in the instantaneous adjustment treatment. Control treatments (using simultaneous matching in discrete time) replicate previous results that exhibit weak or no cycles. Average play is approximated fairly well by Nash equilibrium, and an alternative point prediction, “TASP” (Time Average of the Shapley Polygon), captures some regularities that NE misses. JEL numbers: C72, C73, C92, D83 Keywords: experiments, learning, mixed equilibrium, continuous time. We are grateful to the National Science Foundation for support under grant SES-0925039, and to Sam Wolpert and especially James Pettit for programming support, and Olga Rud, Justin Krieg and Daniel Nedelescu for research assistance. We received useful comments from audiences at the 2012 Contests, Mech- anisms & Experiments Conference at the University of Exeter; Purdue University; and the 2012 Economic Science Association International Conference at NYU. In particular, we want to thank Dieter Balkenborg, Dan Kovenock, Dan Levin, Eyal Winter and Zhijian Wang for helpful suggestions. cason@purdue.edu, http://www.krannert.purdue.edu/faculty/cason/ dan@ucsc.edu, http://leeps.ucsc.edu E.Hopkins@ed.ac.uk, http://homepages.ed.ac.uk/hopkinse/