Prudent Rationalizability and the Best Rationalization Principle

TL;DR

This paper introduces a new cautious reasoning concept called prudent rationalizability for finite sequential games, using belief systems with non-standard probabilities, and shows its equivalence to existing definitions and algorithmic characterization.

Contribution

It formulates prudent rationalizability via belief systems with non-standard probabilities and c-strong belief, extending the solution concept to sequential games with unawareness.

Findings

Proposes a belief-based iterative reduction procedure for prudent rationalizability.

Shows equivalence between the new definition and the original by Heifetz et al. (2021).

Provides an algorithmic characterization via iterated admissibility.

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.