Prudent Rationalizability and the Best Rationalization Principle
Nicodemo De Vito
TL;DR
The paper develops a CNPS-based framework for prudent rationalizability in finite sequential games with perfect recall, introducing c-strong belief as a cautious belief modality. It proves that prudent rationalizability can be characterized algorithmically via iterated admissibility and is equivalent to the original conditional-belief formulation, extending to games with unawareness. The results illuminate epistemic foundations of cautious forward-induction reasoning and connect the belief-reduction approach to standard solution concepts, while offering a bridge to lexicographic rationalizability in static cases. Overall, the work provides a rigorous, non-standard-analysis-based basis for best rationalization in sequential settings.
Abstract
We study cautious reasoning in finite sequential games played by agents with perfect recall. Our contribution lies in formulating a definition of prudent rationalizability (Heifetz et al. 2021, BEJTE) as an iterative reduction procedure of beliefs. To this end, we represent the players' beliefs by systems of conditional non-standard probability measures. The key novelty is the notion of c-strong belief, a non-standard, "cautious" version of strong belief (Battigalli and Siniscalchi 2002, JET). Our formulation of prudent rationalizability embodies a "best rationalization principle" similar to the one that underlies the solution concept of strong rationalizability. The main results show the equivalence between the proposed definition with the one originally put forth by Heifetz et al. (2021) in terms of conditional beliefs represented by standard probabilities. In particular, it is shown that prudent rationalizability can be algorithmically characterized by iterated admissibility. Finally, our formulation can be extended to sequential games with unawareness.