A doxastic behavioral characterization of generalized backward induction

- We introduce dynamic, behavioral models of extensive games.
- States are described in terms of actual choices; strategies play no role.
- Rationality is judged on the basis of the actual beliefs that the player has at the time of choice.
- We provide a doxastic characterization of a generalization of backward induction that does not rely on counterfactuals.

We investigate an extension of the notion of backward induction to dynamic games with imperfect information and provide a doxastic characterization of it. Extensions of the idea of backward induction were proposed by Penta (2009) and later by Perea (2014), who also provided a doxastic characterization in terms of the notion of common belief of future rationality. The characterization we propose, although differently formulated, is conceptually the same as Perea's and so is the generalization of backward induction. The novelty of this contribution lies in the models that we use, which are dynamic, behavioral models where strategies play no role and the only beliefs that are specified are the actual beliefs of the players at the time of choice. Thus players' beliefs are modeled as temporal, rather than conditional, beliefs and rationality is defined in terms of actual choices, rather than hypothetical plans.