Coordination between a sophisticated and fictitious player

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.