Disagreement Under Almost Common Knowledge of Rationality

Abstract

Two agents sincerely exchange their best guesses about the state of the world infinitely many times. When each agent places a small positive probability on the event that her opponent is of some finite level of reasoning and initial disagreement is large enough (that is, private signals are strong and different), permanent and large disagreement is possible even for infinitely sophisticated agents.

Keywords: disagreement, almost common knowledge, level-k reasoning

JEL Classification: D83