Backward Induction Reasoning beyond Backward Induction

• Authors: Antonio Penta.
• BSE Working Paper: 112340 | September 24
• Keywords: Incomplete Information , robustness to bounded rationality , backward induction , backwards procedure , backwards rationalizability , interim perfect equilibrium , perfect bayesian equilibrium rationalizability
• JEL codes: C72, C73, D82
• Incomplete Information
• robustness to bounded rationality
• backward induction
• backwards procedure
• backwards rationalizability
• interim perfect equilibrium
• perfect bayesian equilibrium rationalizability

Backward Induction is only defined for games with perfect information, but its logic is also invoked in many equilibrium concepts for games with imperfect or incomplete information. Yet, the meaning of ‘backward induction reasoning’ is unclear in these settings, and we lack a way to apply its simple logic to general games. We remedy this by introducing a solution concept, Backwards Rationalizability, that satisfies several properties normally ascribed to backward induction reasoning, foremost the possibility of being computed via a tractable backwards procedure. We also show that Backwards Rationalizability characterizes the robust predictions of a ‘perfect equilibrium’ notion that introduces the backward induction logic and nothing more into equilibrium analysis. We discuss a few applications, including a new version of peer-confirming equilibrium (Lipnowski and Sadler (2019)) that, thanks to Backwards Rationalizability, restores in dynamic games the natural comparative statics that the original concept only displays in static settings.