Backward Induction Reasoning beyond Backward Induction

Résumé

Backward Induction is a fundamental concept in game theory. As an algorithm, it can only be used to analyze a very narrow class of games, but its logic is also invoked, albeit informally, in several solution concepts for games with imperfect or incomplete informa-tion (Subgame Perfect Equilibrium, Sequential Equilibrium, etc.). Yet, the very meaning of ‘backward induction reasoning’ is not clear in these settings, and we lack a way to apply this simple and compelling idea to more general games. We remedy this by introducing a solution concept for games with imperfect and incomplete information, Backwards Rational-izability, that captures precisely the implications of backward induction reasoning. We show that Backwards Rationalizability satisfies several properties that are normally ascribed to backward induction reasoning, such as: (i) an incomplete-information extension of subgame consistency (continuation-game consistency); (ii) the possibility, in finite horizon games, of being computed via a tractable backwards procedure; (iii) the view of unexpected moves as mistakes; (iv) a characterization of the robust predictions of a ‘perfect equilibrium’ notion that introduces the backward induction logic and nothing more into equilibrium analysis. We also discuss a few applications, including a new version of peer-confirming equilibrium (Lipnowski and Sadler (2019)) that, thanks to the backward induction logic distilled by Backwards Rationalizability, restores in dynamic games the natural comparative statics the original concept only displays in static settings.

Mots-clés

ackward induction; backwards procedure; backwards rationalizability; incomplete information; interim perfect equilibrium, rationalizability; robustness;