J Econ (2011) 102:263–273 DOI 10.1007/s00712-010-0176-6 Coordination between a sophisticated and fictitious player Bryan C. McCannon Received: 22 February 2010 / Accepted: 22 October 2010 / Published online: 11 November 2010 © Springer-Verlag 2010 Abstract Successful coordination is a common and important social problem. Achieving it relies on the players’ ability to accurately anticipate future choices from known information. Individuals may not only lack this cognitive ability, but differ in it. Fictitious Play is an adaptive behavior where a myopic best response to the historical play of an opponent is selected. I consider the interaction between a fictitious player and a sophisticated player in 2 × 2 coordination games. The existence of coordination, the selection of equilibria, and the payoffs generated are analyzed. Keywords Coordination · Equilibrium selection · Fictitious Play JEL Classification C72 1 Introduction The necessity of coordination is prevalent in many social settings and is a common feature of strategic interaction. Coordination failure arises when individuals fail to select an equilibrium or choose strategies that lead to an equilibrium all find inferior to another. Successful coordination relies on each individual accurately assessing her environment to correctly anticipate her opponent’s selection. Challenges arise if an individual lacks the cognitive ability to do this. Individuals may not have the intelligence needed to derive the full contingency plan that traditional repeated game theory assumes. Some players may use simpler adaptive rules to make Electronic supplementary material The online version of this article (doi:10.1007/s00712-010-0176-6) contains supplementary material, which is available to authorized users. B. C. McCannon (B ) Wake Forest University, Box 7505, Winston-Salem, NC 27109, USA e-mail: mccannbc@wfu.edu 123