Best Response Cycles in Perfect Information Games
13 Pages Posted: 23 Jun 2015
Date Written: May 11, 2015
Abstract
We consider n–player perfect information games with payoff functions having a finite image. We do not make any further assumptions, so in particular we refrain from making assumptions on the cardinality or the topology of the set of actions and assumptions like continuity or measurability of payoff functions. We show that there exists a best response cycle of length four, that is, a sequence (σ0, σ1, σ2, σ3, σ0) of pure strategy profiles where every successive element is a best response to the previous one. This result implies the existence of point-rationalizable strategy profiles. When payoffs are only required to be bounded, we show the existence of an ϵ–best response cycle of length four for every ϵ > 0.
Keywords: Perfect information games, determinacy, best response cycles, rationalizability
JEL Classification: C72
Suggested Citation: Suggested Citation