The power of paradox: some recent developments in interactive epistemology

Paradoxes of game-theoretic reasoning have played an important role in spurring developments in interactive epistemology, the area in game theory that studies the role of the players’ beliefs, knowledge, etc. This paper describes two such paradoxes – one concerning backward induction, the other iterated weak dominance. We start with the basic epistemic condition of "rationality and common belief of rationality" in a game, describe various ‘refinements’ of this condition that have been proposed, and explain how these refinements resolve the two paradoxes. We will see that a unified epistemic picture of game theory emerges. We end with some new foundational questions uncovered by the epistemic program. This survey owes a great deal to joint work and many conversations with Robert Aumann, Amanda Friedenberg, Jerry Keisler, and Harborne Stuart. Scott Ashworth, John Asker, Carliss Baldwin, Heski Bar-Isaac, Pierpaolo Battigalli, Ken Corts, Konrad Grabiszewski, Joe Halpern, Rena Henderson, Martin Meier, Martin Rechenauer, and participants in various seminars provided important input. The associate editor and referees made very helpful suggestions and observations. Financial support from Harvard Business School and the Stern School of Business is gratefully acknowledged.