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 himself. 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 move only once. While strategic-form perfect equilibrium yields backward induction in games where players move only once 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 Independent Dekel-Fudenberg Procedure. Since beliefs are modelled 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.

Keywords: Perfect information games, backward induction paradox, non-Archimedean probabilities, stochastic independence.