Epistemic foundation of the backward induction paradox

Abstract

After having observed a deviation from backward induction, a player might deem the opponent prone to deviate from backward induction again, making it worthwhile to deviate themself. Such reaction might make the deviation by the opponent worthwhile in the first place—which is the backward induction paradox. This argument against backward induction cannot be made in games where all players choose only once on each path. While strategic-form perfect equilibrium yields backward induction in games where players choose only once on each path but not necessarily otherwise, no existing non-equilibrium concept captures the backward induction paradox by having these properties. To provide such a concept, we define and epistemically characterize the concept of independently permissible strategies. Since beliefs are modeled by non-Archimedean probabilities, meaning that some opponent choices might be assigned subjective probability zero without being deemed subjectively impossible, special attention is paid to the formalization of stochastically independent beliefs.

Epistemic foundation of the backward induction paradox