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on Utility Models and Prospect Theory |
| By: | Behrens, Kristian; Murata, Yasusada |
| Abstract: | We characterize the family of utility functions satisfying linear fractional relative risk aversion (LFRRA) in terms of the Gauss hypergeometric functions. We apply this family, which nests various utility functions used in different strands of literature, to monopolistic competition and obtain the profit-maximizing price by generalizing the Lambert W function. We let firm-level data decide whether the RRA in each sector or in the aggregate economy is increasing, decreasing, or constant, which in turn determines whether markups are decreasing, increasing, or constant with respect to marginal costs. |
| Keywords: | Gauss hypergeometric functions |
| JEL: | D43 D21 D22 D11 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20769 |
| By: | Whelan, Karl |
| Abstract: | Ellsberg’s paradox shows that people prefer gambles with known probabilities to those where they are uncertain. Standard explanations rule out risk aversion by appealing to Savage’s (1954) subjective expected utility theory but this axiomatic approach leaves open other interpretations of the evidence. We provide a simpler argument: a routine application of the law of total variance shows that the variance of the payoff from a binary gamble is determined entirely by the mean probability belief, not by uncertainty about those beliefs. Ellsberg-type choices are not consistent with rational mean–variance evaluations of risk. |
| JEL: | D81 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20698 |
| By: | Aluma Dembo; Shachar Kariv; Matthew Polisson; John K. -H. Quah |
| Abstract: | Ellsberg's famous paradox challenged Savage's subjective expected utility theory (EUT) -- which reduces uncertainty to risk -- by suggesting an aversion toward ambiguity. We provide a revealed preference test of the full set of axioms underpinning subjective EUT under uncertainty and compare it to an analogous test of objective EUT under risk. We find that individual choices are as consistent with utility maximization and expected utility maximization under uncertainty as they are under risk. Nevertheless, there is greater empirical scope for non-EUT models under uncertainty than under risk, and the absolute and relative consistency of EUT and non-EUT models vary considerably across subjects. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.09355 |
| By: | Po Hyun Sung; Ben Wincelberg |
| Abstract: | Standard stochastic choice models used to estimate risk aversion can lead to risk-aversion reversals, where a more risk-averse individual chooses a riskier lottery more frequently than a less risk-averse individual. We study when reversals are implied by the preference specification rather than the noise specification. We say that two utilities imply reversals in a given noise framework if reversals arise for every specification of noise for each individual. For weak utility, a flexible class that includes logit and probit and allows for menu-dependent noise, two utilities imply reversals if and only if their curvature ratio is unbounded. This condition holds for CARA, CRRA, and their generalizations, for which reversals arise for empirically relevant coefficients and lotteries, raising concerns about resulting estimates and out-of-sample predictions. Finally, we show that equicautious HARA, sum-ex, and sum-power utilities do not imply reversals and that, moreover, these families remain well-behaved for multinomial choice. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.05686 |
| By: | Riedel, Frank (Center for Mathematical Economics, Bielefeld University); Spengemann, Marco (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We study optimal insurance design under linear transaction costs for a policyholder with smooth ambiguity preferences when the underlying loss distribution is identifiable ex post. Under expected utility, Arrow’s classical theorem implies that the optimal contract is a straight deductible. Under ambiguity, this result generally fails. We show that ex post identifiability restores the straight-deductible structure: the optimal contract consists of model-contingent straight deductibles. We also derive comparative statics with respect to transaction costs and characterize the ordering of deductibles under stochastic ordering of loss distributions. |
| Keywords: | Insurance design, risk sharing, smooth ambiguity aversion, identifiability, straight deductible, comparative statics |
| Date: | 2026–07–22 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:767 |
| By: | Xianhua Peng; Wu Guo |
| Abstract: | We propose the first deep learning algorithm, the Certainty Equivalent Learning (CEL) algorithm, for solving high-dimensional discrete-time dynamic programming problems with recursive utility. Dynamic programming with recursive utility is numerically challenging because the recursive utility does not have an explicit representation and the Bellman equation contains a certainty equivalent that is difficult to evaluate. The CEL algorithm learns this certainty-equivalent value directly with neural networks and jointly approximates value functions, policy functions, and certainty-equivalent functions. The CEL algorithm is mesh-free and simulation-based, allowing high-dimensional state and control spaces, and does not rely on Euler equations, first-order conditions, or differentiability of the state transition function. The CEL algorithm also works for dynamic programming problems with expected utility as expected utility is a special case of recursive utility. We apply the CEL to discounted linear exponential quadratic Gaussian control, small-noise robust control, Epstein-Zin DSGE, and multivariate strategic asset allocation problems. Compared with closed-form and VFI-based benchmarks, the CEL delivers accurate value and policy approximations, remains effective in high-dimensional problems, achieves accuracy comparable to VFI in the small-noise robust-control case, and produces out-of-sample Bellman errors and Euler or first-order residuals that are in the range from 1.0e-4 to 1.0e-3 for most problems. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.04278 |
| By: | Xianhua Peng; Wu Guo; Songyan Wang; Jianfei Zhu |
| Abstract: | This paper proposes the certainty-equivalent first-order learning (CEFOL) algorithm, a deep learning algorithm for solving discrete-time dynamic programming problems with recursive utility. Dynamic programming with recursive utility is challenging because nonlinear certainty equivalent appears in the Bellman equation and the first-order optimality conditions but is difficult to evaluate. By introducing a separate neural network to represent the certainty equivalent, CEFOL enables the exploitation of the Bellman and model-specific first-order optimality conditions. In addition to certainty equivalent, CEFOL also uses neural networks to learn the value functions, policy functions, and Lagrange multipliers by using model-specific first-order conditions to construct residuals for minimization. By using first-order and KKT residuals to learn the policy, CEFOL directly accommodates general equality and inequality constraints on the controls, including occasionally binding constraints, without requiring penalty functions or problem-specific reformulations. We apply the algorithm to risk-sensitive and Epstein--Zin consumption-saving problems, a small-noise robust-control problem, and a DSGE model with recursive preferences and stochastic volatility. Across these applications, out-of-sample Bellman diagnostics and model-specific optimality residuals, including Euler or first-order residuals where applicable, are generally of order 1.0e-4 to 1.0e-3 over the relevant state regions, with larger values mainly near binding constraints, and the learned value and policy functions closely match VFI benchmarks when available. The CEFOL algorithm also works for dynamic programming problems with expected utility, as expected utility is a special case of recursive utility. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.09461 |
| By: | Madhuparna Karmokar; Ujjwal Kumar; Soumyarup Sadhukhan |
| Abstract: | We study unanimous and strategy-proof probabilistic social choice correspondences (PSCCs), where the selected set of alternatives is interpreted as an interim outcome, and agents evaluate sets using conditional expected utility. We analyze two preference domains introduced by Barbera et al. (2001): the conditionally expected utility consistent (CEUC) domain and the conditionally expected utility consistent with equal probabilities (CEUCEP) domain. Our results characterize all unanimous and strategy-proof PSCCs on these domains and identify cases when randomization enlarges the class of admissible rules. On the CEUC domain, every unanimous and strategy-proof PSCC is a random dictatorship, showing that randomization over sets yields no additional flexibility. In contrast, the CEUCEP domain admits a richer family of unanimous and strategy-proof PSCCs. For at most three agents, these rules are precisely the random bi-dictatorial rules, which are convex combinations of bi-dictatorial rules introduced in Feldman (1980). For four or more agents, the characterization depends on the number of alternatives. When there are exactly three alternatives, the class expands to the larger family of coalition-weighted rules. Thus, randomization enlarges the class of strategy-proof correspondences in the three-alternative case, producing rules that are not convex combinations of deterministic strategy-proof correspondences. However, for four or more alternatives, the class of unanimous and strategy-proof probabilistic correspondences again collapse to random bi-dictatorships. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.03955 |
| By: | Asen Kochov |
| Abstract: | The paper shows that in a dynamic setting with multiple sources of uncertainty, recursive ambiguity-averse preferences may imply a preference for late resolution of uncertainty. In particular, the simultaneous resolution of two sources can offer hedging benefits that are negated when one source is resolved earlier and uncertainty is evaluated recursively. The paper illustrates the mechanism in a simple dynamic urn problem. In a special case, an equivalent static formulation involving composite bets on two urns suggests a direct experimental test. |
| Keywords: | ambiguity, recursive utility, timing attitudes |
| JEL: | D81 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12804 |
| By: | Cheaheon Lim; Tomasz Strzalecki |
| Abstract: | The classical expected utility (EU) axioms are not sufficient for finite datasets. There are a number of anomalies (violations of EU) where axioms are satisfied. This paper studies axioms that are immune to this problem and definitively delineate between EU and non-EU. We discuss implications for experimental design and explore the automatic generation of anomalies. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.15740 |
| By: | David Lowing (ENS Rennes - École normale supérieure - Rennes, CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique); Satoshi Nakada (Tokyo University of Science); Florian Navarro (GRANEM - Groupe de Recherche Angevin en Economie et Management - UA - Université d'Angers - Institut Agro Rennes Angers - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement) |
| Abstract: | In cooperative games with transferable utility (TU-games), a player's contribution may vary depending on the coalition they join, reflecting different levels of synergy with other members. In this paper, we introduce a family of axioms referred to as sub-game order preservation axioms, which formalize the intuition that a player's payoff should increase with the degree of synergy they exhibit within a coalition. We propose four distinct axioms, each of which captures a different interpretation of what constitutes synergy in the context of transferable utility. We demonstrate that one of these variants is incompatible with the classical Efficiency axiom, thereby giving rise to an impossibility result. The remaining three axioms, when combined with Efficiency, lead to unique characterizations of three well-known solution concepts: the Shapley value, the Center of the Imputation Set (CIS), and the Equal Allocation of Non-Separable Contributions (ENSC) value, respectively. |
| Keywords: | CIS value, ENSC value, TU-games, Sub-game order preservation, Shapley value |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05153554 |
| By: | Rui Yao; Kenan Zhang |
| Abstract: | Large-scale traffic assignment requires equilibrium models that are both behaviorally plausible and computationally tractable. This paper develops a perturbed utility Markovian equilibrium (PUME) framework that preserves the scalability of link-based Markovian traffic equilibrium models and extends their applicability to settings with boundary choice probabilities, undiscounted network loading, and general link interactions. As the behavioral basis of PUME, we first develop the perturbed utility Markovian choice model (PUMCM) in which the Bellman optimality operator is defined through a convex surplus function whose gradient directly yields the optimal policy. The model generalizes existing additive random utility (ARUM) Markovian choice models and admits both interior and boundary choice probabilities. Accordingly, unattractive links can receive zero flow without imposing ex ante choice-set restrictions as in existing ARUM models. We establish conditions under which the corresponding Markov decision problem is well posed and yields a proper demand mapping. We then formulate the equilibrium as a variational inequality (VI) problem on the dual cost space and establish its existence and uniqueness. Particularly, the VI formulation of PUME accommodates non-separable and asymmetric cost structures and thus offers a more flexible modeling framework than existing Markovian traffic equilibrium (MTE) models. For computation, we develop a modified policy iteration method for network loading and a safeguarded accelerated meta-algorithm for computing equilibrium. Both algorithms are proven to be globally convergent and have demonstrated satisfactory numerical performances. Experiments on benchmark and synthetic networks further show that the proposed framework is highly scalable and robust towards a wide variety of demand-supply settings. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.09568 |
| By: | Bénabou, Roland; Henkel, Luca |
| Abstract: | We review the economic literature on self-image, which conceptualizes identity as a set of beliefs about one’s core traits, values, goals, and social ties. Self-image concerns lead individuals to process information and make choices in non-standard ways that help affirm and protect certain valued identities. We first present the main cognitive mechanisms involved within a simple unifying framework. We then survey the extensive laboratory, online, and field experimental literature on the nature and behavioral implications of self-image concerns. We discuss in particular how they give rise to information and decision avoidance, motivated memory and beliefs, excuse-driven behavior, preferences for truth-telling, hypothetical bias, moral cleansing and moral licensing, collective identities, political preferences, and other forms of self-signaling or self-deception. We subsequently discuss common empirical strategies used to identify self-image concerns, as well as the threats to their validity and how to alleviate them. We conclude by outlining open questions and directions for future research on the belief-based approach to identity. |
| Keywords: | Self-image; Identity; Motivated beliefs; Belief-based utility; Behavioral economics; Experimental economics |
| JEL: | D64 C90 D83 |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20663 |
| By: | Masaaki Fujii (Faculty of Economics, The University of Tokyo) |
| Abstract: | This work solves the equilibrium price formation problem for the risky stock by combining mean-field game theory with the binomial tree framework, adapting the classic approach of Cox, Ross & Rubinstein. For agents with exponential and recursive utilities of exponential-type, we prove the existence of a unique mean-field market-clearing equilibrium and derive an explicit analytic formula for equilibrium transition probabilities of the stock price on the binomial lattice. The agents face stochastic terminal liabilities and incremental endowments that depend on unhedgeable common and idiosyncratic factors, in addition to the stock price path. We also incorporate an external order flow. Furthermore, the analytic tractability of the proposed approach allows us to extend the framework in two important directions: First, we incorporate multi-population heterogeneity, allowing agents to differ in functional forms for their liabilities, endowments, and risk coefficients. Second, we relax the rational expectations hypothesis by modeling agents operating under subjective probability measures which induce stochasti- cally biased views on the stock transition probabilities. Our numerical examples illustrate the qualitative effects of these components on the equilibrium price distribution. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:tky:fseres:2026cf1276 |
| By: | Ram Sewak Dubey |
| Abstract: | In this paper we examine the constructive nature of social welfare orders on infinite utility streams $X=Y^{\mathbb{N}}$ satisfying Strong Equity, Hammond Equity, or the Pigou--Dalton transfer principle. The constructive social welfare orders are described using lexicographic preference relations. Social welfare orders satisfying Strong Equity, Hammond Equity, or the Pigou--Dalton transfer principle admit explicit descriptions when $Y( |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.23428 |
| By: | Eden, Maya; Piacquadio, Paolo G. |
| Abstract: | Are people's ethical views informative about what is actually ethical? We show that, when the social preference relation is Paretian, it must closely mirror people's ethical views. In particular, people's aversion to income inequality among strangers places tight bounds on the admissible inequality attitudes of the social welfare function. Our results also suggest a new rationale for paternalism: if people are paternalistic about the choices of others, then the social welfare function must be paternalistic as well. |
| Keywords: | Paternalism; Pareto; Inequality aversion |
| JEL: | D30 D60 D90 |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:20624 |
| By: | Stefano BOSI; Riccardo BUSO; David DESMARCHELIER |
| Abstract: | We reconsider the pollution-fertility interplay in light of the e§ect of pollution on the marginal utility of consumption in a simple overlapping generations economy. Each household lives two periods. During the youth, the agent divides her time between work and raising children. Income from work is saved and consumed in retirement. The old are also exposed to a pollution externality generated by production activities. The state finances pollution abatement expenditures through a proportional tax levied on production. Notable results emerge, both in the short and long run. In the long run, a higher green-tax rate decreases (increases) the population size when household environmental concerns are low (high). Surprisingly, in the case of higher environmental concern, as the data show, environmental policy can help counter the demographic decline being experienced, notably, by the European Union. In the short run, endogenous áuctuations can arise around the unique steady state when pollution increases the marginal utility of consumption (the so-called compensation effect). More precisely, a persistent twoperiod cycle can emerge through a flip bifurcation, or a limit cycle through a Neimark-Sacker bifurcation. Interestingly, the equilibrium becomes locally indeterminate in the vicinity of the limit cycle, which promotes selffulfflling expectations and greater macroeconomic instability. |
| Keywords: | Overlapping generations model; flip and Neimark-Sacker bifurcations; local indeterminacy; pollution; endogenous fertility. |
| JEL: | C62 H23 O44 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ulp:sbbeta:2026-25 |
| By: | Yu-Ting Ho |
| Abstract: | We study competition among multiple firms that offer differentiated varieties of the same good to a unit-demand agent. The agent has heterogeneous valuations for goods from different firms. Firms do not observe the agent's exact valuations, but they know their distribution. Firms simultaneously post menus of contracts, after which the agent chooses a firm and one of its contracts to maximize her utility. This defines a game in which firms aim to maximize expected revenue. We introduce a sufficient condition, density-regularity, under which each firm's best response to any arbitrary menu profile posted by its opponents is equivalent to posting a menu that contains only a posted-price contract. Our result is not a direct extension of the canonical Myersonian model with a single seller. The standard argument in the literature breaks down once heterogeneous preferences and competition are introduced. We therefore adopt an optimal-control approach, in which the density-regularity condition is essential for establishing the optimality of posted prices. When this condition fails, posted prices may fail to be a best response. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.22720 |
| By: | Vorchik, Andrey |
| Abstract: | This article is devoted to the phenomenon of intrinsic motivation, to understand which two models are proposed. We study how positive/negative intrinsic motivation to work (experienced utility) affects worker's individual labour supply (model I) and the amount of effort they exert (model II). In model I, we use intrinsic motivation to explain the positive/negative slope and possible bending of the individual labor supply curve. Both models I and II show that positive intrinsic motivation to work (job satisfaction) removes the tradeoff between worker's happiness and efficiency. Thus, from an evolutionary point of view, the very possibility of being intrinsically motivated for any kind of activity can be considered as an adaptation that gives its owner an evolutionary advantage. Provided that probabilities of achieving internal and external goals of the person are positively correlated, higher intrinsic motivation is also contributing to the achievement of the external goal of survival in the environment. However, as follows from model II, in order to persist in the long term, intrinsic motivation must not only be positive, but also high enough so that it is not crwoded out by extrinsic motivation in the course of cultural selection. The paper explains the mechanisms behind crowding out and the reverse process of crowding in, as well as describes methods of regulating these processes. The negative effects of crowding out on the efficiency labour markets and the economy as a whole are discussed, as well as practical implications for the education system. |
| Keywords: | rationalization theory by Max Weber, extrinsic and intrinsic motivation, experienced utility theory by Daniel Kahneman, Bernoulli utility function, emotions, cultural selection, self-fulfilling prophecy |
| JEL: | B52 D03 D61 J20 M52 |
| Date: | 2026–03–26 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:128463 |
| By: | Zijun Meng |
| Abstract: | This paper studies a cheap-talk model of strategic test announcements. A teacher observes the day of the test of the next week decided by the nature and makes an announcement to his students who choose effort levels of studying. The competing forces are the teacher's value on consistent study habits and the students' grade orientation. We characterize the pure strategy Nash equilibrium under the linear-quadratic student utility. We also study what happens when the teacher can commit to an information policy. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.22434 |
| By: | Jason Hawkins; Omid Armantalab |
| Abstract: | Travel behavior and demand modeling seeks to understand the factors that motivate transportation decisions. At the same time, the field is increasingly adopting algorithmic and artificial intelligence (AI) tools that improve predictive accuracy, often at the cost of a grounding in hypothesis-based theory validation and behavioural explanation. In this discussion paper, we use goal pursuit theory (GPT) to illustrate why behavioral theory is a necessary complement to prediction in travel behavior research. Unlike random utility maximization (RUM) or close alternatives (e.g., random regret minimization (RRM)), GPT explicitly models how travelers (1) activate context-dependent goals (hedonic, gain, normative), (2) resolve conflicts between competing objectives, and (3) make sequential decisions across temporal scales. We demonstrate GPT's merits through three transport applications: activity scheduling (handling hierarchical goal structures), vehicle ownership (disentangling bundled mobility goals), and location choice (capturing latent goal interactions via matrix factorization). We provide actionable guidance for implementation, including: (a) hybrid choice model specifications linking goals to observable behaviors, (b) parallels to complementary behavioral theories from the transportation field, and (c) data requirements and comparative benchmarks against RUM/RRM models. |
| Date: | 2026–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2606.29145 |
| By: | Han Feng; Difang Huang; Jue Wang; Zhengjun Zhang |
| Abstract: | We explain the long-standing puzzle of na\"ive diversification with a simple, testable condition: equal weighting is minimum-variance optimal when the forecast-error covariance matrix has a uniform eigenstructure. This "Golden Criterion" drives a two-stage adaptive strategy that dynamically blends naive and optimized weights based on the empirical distance from this condition. Applied to U.S. equity premium forecasting, the method delivers consistent out-of-sample gains in forecast accuracy, utility, and Sharpe ratios. Diversity-driven shrinkage dominates at short horizons, while optimized weights regain their edge at longer horizons, offering clear horizon-dependent guidance for portfolio construction. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.11054 |
| By: | Hongsilp Sriket; Navarat Temsumrit |
| Abstract: | This paper examines the heterogeneous effects of population aging on sectoral employment reallocation across countries at varying stages of economic development. Using an unbalanced panel dataset of 59 countries spanning 1960–2018, we estimate a panel fixed-effects model in which the old-age dependency ratio serves as the primary explanatory variable for employment shares across agriculture, manufacturing, and services. To rationalize the empirical findings, we develop an extended overlapping generations (OLG) model incorporating hierarchical consumption preferences differentiated by age cohort, building on the non-homothetic utility frameworks of Matsuyama (2002) and Foellmi and Zweimüller (2008). The model generates age-specific demand structures in which older cohorts systematically shift consumption expenditure toward services, particularly health-related services, inducing labor reallocation away from industry. Empirical results confirm that aging accelerates tertiarization – the expansion of service-sector employment share – most prominently in high-income economies, consistent with the demand-side channel of structural transformation. In low-income countries, however, binding income constraints prevent full materialization of preference-driven sectoral reallocation, resulting in persistent agricultural employment retention. Middle-income countries exhibit ambiguous dynamics, suggestive of a structural transformation puzzle. These findings highlight that the demographic transition interacts with the level of economic development to shape the trajectory of deindustrialization and de-agriculturalization, with important implications for development policy and long-run labor productivity growth. |
| Keywords: | Structural Transformation; Cross-country Analysis; Aging population; Human Capital |
| JEL: | O11 O40 O57 |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:pui:dpaper:261 |