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.

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 paper addresses the inefficiency and fragility of conventional stated-preference experiments for probabilistic choices, where ex ante expected returns and willingness-to-pay (WTP) estimates rely on multiple choice rounds and strong parametric assumptions—leading to lengthy surveys and low feasibility for ex ante policy evaluation. We propose a nonparametric identification method requiring at most two probabilistic choices per respondent. It imposes no functional-form assumptions on utility and, for the first time, fully identifies both the population distribution of ex ante expected returns and WTP for structured preference objects (e.g., multidimensional job attributes). Theoretical foundations integrate nonparametric identification theory with structured discrete choice modeling. Applied to elite student employment preferences in Côte d’Ivoire, the method robustly identifies a significant upward effect of public-sector jobs on private-sector hiring costs—demonstrating both empirical validity and direct policy relevance.

This paper studies collective aggregation of individual budget distributions in multi-dimensional budget allocation, focusing on mechanism design within the star-shaped preference domain. Method: We introduce a novel star-shaped utility function based on share ratios and analyze mechanisms—including the Nash product maximization mechanism and the uniform phantom mechanism—under various distance metrics (e.g., ℓ₁, ℓ₂). Contribution/Results: We establish the first mechanism achieving simultaneous Pareto efficiency, group strategyproofness, and core fairness in multi-option settings. We characterize the Nash product maximization mechanism as both group strategyproof and core fair. For two alternatives, we prove the uniform phantom mechanism is the unique rule satisfying all three properties; however, under ℓ₁ or ℓ₂ distances, no mechanism can satisfy all three in settings with three or more alternatives. Finally, we construct a computationally tractable mechanism that ensures both fairness and efficiency, offering a new paradigm for budget aggregation that balances theoretical rigor with practical implementability.

This paper studies the multidimensional Bayesian utility maximization problem under unit-demand settings where buyers’ valuations for items are independent and identically distributed (i.i.d.). It designs prior-independent mechanisms to approximate the social welfare benchmark. Methodologically, it extends the Hartline–Roughgarden single-dimensional analysis framework to the multidimensional setting, establishing a general information-theoretic reduction from multidimensional unit-demand environments to homogeneous-item settings. Theoretically, it proves tight approximation guarantees: a $(1-1/e)$-approximation when the number of items $m$ is at least the number of buyers $n$, and a tight $Theta(log(n/m))$-approximation when $n > m$. These results uncover counterintuitive structural complexity in multidimensional utility maximization and establish fundamental limits on the approximability of social welfare—revealing both its intrinsic difficulty and optimality as a benchmark.

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 study addresses the challenge of explaining and predicting aggregate consumption behavior and achieving fair resource allocation without access to individual utility information. The authors propose a Constructive Rationalization Method (CRM) that constructs an auxiliary market populated by artificial consumers endowed with easily computable demand functions. By dynamically adjusting the number of artificial consumers and their wealth allocations based on observed aggregate demand, CRM approximates real-market behavior. This approach provides the first generalization risk guarantee for learning aggregate demand functions and achieves an approximation of proportional fairness—all while preserving individual privacy and eschewing any reliance on individual-level utility data. Empirical results demonstrate that CRM effectively predicts group-level consumption patterns and yields resource allocations closely aligned with proportional fairness.

This work addresses the challenge of optimizing collective utility in multi-agent Markov decision processes where agents exhibit heterogeneous time preferences—captured by distinct discount factors and reward functions—rendering conventional single-discount models inadequate. Focusing on utilitarian social welfare, defined as the sum of all agents’ utilities, the paper proposes a finite-memory strategy synthesis method. Theoretical analysis shows that while optimal policies are no longer positional, they can be realized by pure finite-memory counting strategies requiring only polynomial memory in the system size. In contrast, restricting to positional strategies not only incurs a loss in social welfare but also renders the associated threshold decision problem NP-hard. The study thus achieves polynomial-time optimal strategy synthesis and reveals a fundamental trade-off between social welfare and computational complexity inherent in positional strategies.

This study addresses the challenge of welfare maximization under budget constraints in electricity markets, where users’ optimization problems are typically non-convex and difficult to solve. The authors propose an explicit piecewise-modified utility function constructed by splicing the original utility with a logarithmic function, thereby transforming the problem into a convex optimization formulation under tight budget constraints. Leveraging this reformulation, they establish the existence and uniqueness of a competitive equilibrium and demonstrate its equivalence to the solution of the modified convex welfare maximization problem. A dual ascent algorithm is employed to compute the equilibrium, and its convergence—along with the validity of the resulting equilibrium—is corroborated through theoretical analysis and numerical experiments using quadratic and square-root utility functions.