The power of paradox: some recent developments in interactive epistemology

Abstract

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.