utility function specification

This study addresses the lack of empirical grounding in utility function modeling for budget aggregation. Through structured, controlled experiments and rigorous statistical analysis, we systematically evaluate the explanatory power of mainstream utility models—including ℓ₁, ℓ₂, and Leontief—against real human preferences. Results show that conventional distance-based and min-based models exhibit poor fit; most participants’ choices significantly violate their core assumptions. In contrast, peak-linear utility and star-shaped preferences achieve high empirical consistency and satisfy key behavioral properties such as sign symmetry and weak monotonicity. These findings challenge foundational assumptions in mechanism design theory and provide the first large-scale experimental evidence supporting a behaviorally realistic alternative modeling framework for budget aggregation.

How to rigorously prove that any preference relation satisfying completeness, transitivity, continuity, and independence must be representable by an expected utility function, per the von Neumann–Morgenstern (vNM) Expected Utility Theorem? Method: We introduce a fine-grained formalization of the independence axiom and employ a constructive proof strategy, integrating real analysis and decision theory within Lean 4 via its standard library and a formal algebraic model of probabilistic lotteries. Contribution/Results: (1) The first fully machine-checked, end-to-end formalization of the vNM theorem—covering both existence and uniqueness of the utility representation; (2) a more precise characterization of equivalence at decision boundaries, refining the classical statement; and (3) a reusable, foundational formalization of decision theory, designed for applications in economic modeling, AI alignment, and trustworthy decision systems.

This study investigates the preservation and transfer of optimality properties in dynamic programming problems under diverse preference structures. By introducing conjugacy theory from dynamical systems and order-isomorphism techniques, it establishes, for the first time, rigorous equivalence relations among Epstein–Zin preferences, multiplicative Kreps–Porteus preferences, and risk-sensitive preferences, thereby enabling the cross-model transfer of optimality characteristics. This unified framework not only provides a coherent characterization of optimality across multiple preference specifications but also significantly enhances computational accuracy in applied settings: when implemented in a multisector real business cycle model, it improves the numerical precision of value function approximation by up to two orders of magnitude.

This study addresses the problem of extracting an optimal subplan from an existing plan under a budget constraint, while preserving the original actions and their execution order. The goal is to identify a subplan that respects a given cost upper bound, remains executable, and maximizes utility. The decision variant of this problem is proven to be NP-complete. To tackle it, the authors propose a refined integer linear programming (ILP) formulation that significantly reduces model size and enhances computational efficiency without sacrificing solution accuracy. Together with over-subscription planning (OSP), this ILP approach constitutes one of two exact solution methods. Compared to prior work, the proposed ILP method demonstrates marked improvements in both scalability and empirical performance.

This paper formalizes Herbert Simon’s bounded rationality and satisficing decision theory to bridge the mathematical gap between behavioral economics and classical expected utility theory. To this end, we propose the Flexible First-Order Stochastic Dominance (FFSD) framework and achieve the first machine-checked verification of bounded rationality in the Lean 4 theorem prover. Our approach introduces a parameterized tolerance threshold ε < 1/2 to ensure reference-point uniqueness, proves that FFSD is equivalent to expected utility maximization under an approximate indicator function, and generalizes the result to multidimensional decision settings. This work establishes the first verifiable formal foundation for bounded rationality, enabling mechanized reasoning about uncertain decisions under cognitive constraints. It provides a novel, rigorous paradigm for the formal analysis of behavioral economic models.

This work addresses budget-constrained procurement mechanism design by moving beyond the conventional focus on maximizing the buyer’s value alone, instead targeting the buyer’s utility, social welfare, and more general objectives under both prior-free and Bayesian settings. The key contribution is the first mechanism that achieves near-optimal buyer utility while satisfying ex-post budget feasibility, which is further extended to accommodate generalized objective functions. By integrating techniques from mechanism design, Bayesian optimization, worst-case analysis, and budget constraint transformation, the proposed approach yields a constant-factor approximation for social welfare and achieves near-optimal performance for utility objectives under both expected and ex-post budget constraints.

This study addresses the empirical validity of the discounted expected utility (DEU) model in risky intertemporal choice contexts by proposing a nonparametric revealed-preference test. The approach provides the first complete axiomatic characterization of DEU with concave utility, requiring no prior assumptions about the functional forms of either the utility or discount functions, thereby rendering the model empirically falsifiable. Applying this method to existing behavioral experimental data, the analysis reveals that the DEU model is overwhelmingly rejected across most settings, indicating its limited explanatory power in real-world decision-making. These findings underscore both the empirical utility and theoretical novelty of the proposed framework in identifying fundamental limitations of canonical models of intertemporal risk preferences.

This work addresses the longstanding absence of reusable, machine-verifiable formal libraries in computational economics—encompassing game theory, mechanism design, and social choice—by presenting the first systematic effort to develop an open-source formalization in the Lean 4 theorem prover. The library captures core definitions and theorems from these fields and integrates AI-assisted tools to facilitate large-scale mathematical formalization. Beyond providing machine-checkable representations of classical economic theories, the project demonstrates the feasibility and promise of AI-supported formal methods in economic research. This contribution establishes a novel paradigm for future endeavors in formal modeling and automated reasoning within economics, enhancing rigor, reproducibility, and scalability in theoretical exploration.

This study addresses the limitations of traditional urban integration models in capturing household trade-offs under dual constraints of time and money. Building on household production theory, the authors develop a microeconomic framework that jointly models transportation and land-use choices, innovatively incorporating a parallel-constrained multiple discrete-continuous extreme value (PC-MDCEV) structure to accommodate multi-person households. The model endogenously accounts for minimum travel time required for activities as a measure of accessibility, deducting it directly from the household time budget. Empirical analysis using data from the Greater Toronto Area reveals significant economies of scale in household production with respect to time and demonstrates that housing type profoundly influences both time allocation and consumption patterns.

This study addresses risk measurement for financial positions in spaces of Lipschitz functions lacking constant terms and Banach lattice structure. Taking Lipschitz functions vanishing at a reference state as the natural domain, it pioneers a dual representation framework by integrating Lipschitz-free spaces with optimal transport theory. The approach overcomes the absence of cash-additivity through an additive mechanism based on benchmark deviations. This methodology not only yields a unified risk measurement model applicable to complex financial settings—such as path-dependent payoffs, temporal cash flows, and network structures—but also extends to scenarios involving model uncertainty. Within this broader context, the paper successfully derives dual representations for both convex and coherent risk measures, substantially expanding the applicability of classical risk measurement theory.