2025/07/02 by Jingyuan Li, Lin Zhou, Li, Jingyuan +1
Decision Sciences · Economics, Econometrics and Finance · #Computational Engineering #Decision-Making and Behavioral Economics #Economic Theory and Institutions #FOS: Computer and information sciences #FOS: Economics and business #Finance #Game Theory and Applications #Mathematical Finance (q-fin.MF) #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2507.07052
openalex publication_date 2025/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces Flexible First-Order Stochastic Dominance (FFSD), a mathematically rigorous framework that formalizes Herbert Simon's concept of bounded rationality using the Lean 4 theorem prover. We develop machine-verified proofs demonstrating that FFSD bridges classical expected utility theory with Simon's satisficing behavior through parameterized tolerance thresholds. Our approach yields several key results: (1) a critical threshold ε < 1/2 that guarantees uniqueness of reference points, (2) an equivalence theorem linking FFSD to expected utility maximization for approximate indicator functions, and (3) extensions to multi-dimensional decision settings. By encoding these concepts in Lean 4's dependent type theory, we provide the first machine-checked formalization of Simon's bounded rationality, creating a foundation for mechanized reasoning about economic decision-making under uncertainty with cognitive limitations. This work contributes to the growing intersection between formal mathematics and economic theory, demonstrating how interactive theorem proving can advance our understanding of behavioral economics concepts that have traditionally been expressed only qualitatively.