WHAT HAPPENED TO THE THREE-LEGGED CENTIPEDE GAME?

Abstract

Abstract In the last two decades, several frameworks have been proposed to analyze the question of whether common knowledge of rationality is sufficient to justify the play of backward induction (BI) in games of perfect information. Three strands of literature have addressed this issue: the literature on equilibrium refinements, the literature on knowledge-based epistemology and the literature on interactive epistemology. This paper surveys seminal frameworks within the first two strands of research and assesses the extent to which they provide a satisfactory solution to the problem. These approaches are illustrated using a three-legged version of Rosenthal's centipede game, which is the classical example in the literature. The paper argues that some of these frameworks provide sensible answers to the riddle of BI or, at least, succeed in bringing the paradox to another level. The paper also points at consistency problems in the body of refinements of Nash equilibrium revealed by the surveyed literature.