Fictitious play in 2×2 games: A geometric proof of convergence

Summary This paper provides a new proof of Miyasawa's (1961) result showing the convergence of fictitious play in 2×2 games. The novelty of the approach used here is that it rests entirely on the geometric properties of the best-response correspondence. The geometric approach greatly shortens the exposition, and it suggests some possible extensions to more difficult convergence conjectures.We thank Glenn Ellison, Vijay Krishna, Eric Maskin and an anonymous referee for helpful comments. This paper was written while Metrick was supported by an NSF Graduate Fellowship and Polak was supported by a Junior Fellowship in the Society of Fellows at Harvard University.