2025/11/27 by De Vito, Nicodemo
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Game Theory and Applications #Game Theory and Voting Systems #Logic, Reasoning, and Knowledge
paper · doi:10.48550/arxiv.2511.22388
openalex publication_date 2025/11/27 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
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.