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on Utility Models and Prospect Theory |
| By: | Lorenzo Bastianello (Universite Paris 2 Pantheon-Assas, LEMMA, Paris, France); Alain Chateauneuf (IPAG Business School, Paris, France and Paris School of Economics and Universite Paris 1, Paris, France); Bernard Cornet (Department of Economics, University of Kansas, Lawrence, KS 66045, USA) |
| Abstract: | Two acts are comonotonic if they co-vary in the same direction. The main purpose of this paper is to derive a new characterization of Cumulative Prospect Theory (CPT) through simple properties involving comonotonicity. The main novelty is a concept dubbed gain-loss hedging: mixing positive and negative acts creates hedging possibilities even when acts are comonotonic. This allows us to clarify in which sense CPT differs from Choquet expected utility. Our analysis is performed under the assumption that acts are real-valued functions. This entails a simple (piece-wise) constant marginal utility representation of CPT, which allows us to clearly separate the perception of uncertainty from the evaluation of outcomes. |
| Keywords: | Cumulative Prospect Theory, Comonotonicity, Gain-loss hedging, Sipos integral, Choquet integral. |
| JEL: | D81 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:kan:wpaper:202511 |
| By: | Somdeb Lahiri |
| Abstract: | We interpret a fuzzy set as a random availability function and provide sufficient conditions under which a preference relation over the set of all random availability functions can be represented by a utility function. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.18863 |
| By: | Cuong Le Van (CNRS, PSE, CES); Ngoc-Sang Pham (EM Normandie) |
| Abstract: | We study the existence of equilibrium when agents' preferences may not beconvex. For some specific utility functions, we provide a necessary and sufficientcondition under which there exists an equilibrium. The standard approach cannot be directly applied to our examples because the demand correspondence of some agents is neither single-valued nor convex-valued. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.16890 |
| By: | Marc Fleurbaey (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Stéphane Zuber (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | How can social prospects be evaluated and compared when there may be a risk on i) the actual allocations that people will receive, ii) the existence of these future people, and iii) their preferences? This paper investigates this question, which can arise when considering policies, such as climate policy, that affect people who do not yet exist. We start from the observation that there is no social ordering that meets minimal requirements of fairness, social rationality, and respect for people's ex ante preferences. We explore three ways around this impossibility. First, if we drop the ex ante Pareto requirement, we can obtain fair ex post criteria that take an (arbitrary) expected utility of an equally-distributed equivalent level of well-being. Second, if the social ordering is not an expected utility, we can obtain fair ex ante criteria that evaluate uncertain individual prospects with a certaintyequivalent measure of well-being. Third, if we accept that interpersonal comparisons rely on VNM utility functions even in absence of risk, we can construct expected utility social orderings that satisfy of a version of Pareto ex ante. |
| Keywords: | Fairness, Social risk, Intergenerational equity |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:hal:cesptp:halshs-05053424 |
| By: | Aase, Knut K. (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | We consider optimal risk sharing in a dynamic setting, where agents have preferences represented by translation invariant recursive utility. This model has some appealing features, both compared to the scale invariant one and to the standard model with expected utility. First, the model allows for a treatment of heterogeneous preferences. This leads to extensions in more realistic directions of the standard, one-period risk sharing model. Second, the new endogenous variable entering the state price deflator is a traded security, an annuity, while in the scale invariant model the corresponding variable is the agent’s wealth. The model invites for a closer look at the mutuality principle in syndicates and optimal risk sharing in society. We also embed a stock market in our setting and derive a consumption based capital asset pricing model. |
| Keywords: | Recursive utility; translation invariant model; utility gradients; optimal risk sharing; CCAPM; optimal risk sharing; the mutuality principle |
| JEL: | D51 D53 D90 E21 G10 G12 |
| Date: | 2025–05–09 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:nhhfms:2025_015 |
| By: | Nicole B\"auerle; Tamara G\"oll |
| Abstract: | In this paper, we consider $n$ agents who invest in a general financial market that is free of arbitrage and complete. The aim of each investor is to maximize her expected utility while ensuring, with a specified probability, that her terminal wealth exceeds a benchmark defined by her competitors' performance. This setup introduces an interdependence between agents, leading to a search for Nash equilibria. In the case of two agents and CRRA utility, we are able to derive all Nash equilibria in terms of terminal wealth. For $n>2$ agents and logarithmic utility we distinguish two cases. In the first case, the probabilities in the constraint are small and we can characterize all Nash equilibria. In the second case, the probabilities are larger and we look for Nash equilibria in a certain set. We also discuss the impact of the competition using some numerical examples. As a by-product, we solve some portfolio optimization problems with probability constraints. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.20340 |
| By: | Ho Ka Chan; Taro Toyoizumi |
| Abstract: | People often deviate from expected utility theory when making risky and intertemporal choices. While the effects of probabilistic risk and time delay have been extensively studied in isolation, their interplay and underlying theoretical basis are still under debate. In this work, we applied our previously proposed anticipated surprise framework to intertemporal choices with and without explicit probabilistic risk, assuming that delayed reward may fail to materialize at a fixed hazard rate. The model prediction is consistent with key empirical findings: time inconsistency and aversion to timing risk stem from the avoidance of large negative surprises, while differences in mental representations of outcome resolution explain the conflicting effects of probabilistic risk on temporal discounting. This framework is applicable to a broad range of decision-making problems and offers a new perspective over how various types of risk may interact. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.19514 |
| By: | Daniel L. Chen (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | Ambiguity aversion is the interpretation of the experimental finding (the Ellsberg paradox) that most subjects prefer betting on events whose probabilities are known (objective) to betting on events whose probabilities are unknown (subjective). However in typical experiments these unknown probabilities are known by others. Thus the typical Ellsberg experiment is a situation of asymmetric information. People may try to avoid situations where they are the less informed party, which is normatively appropriate. We find that eliminating asymmetric information in the Ellsberg experiment while leaving ambiguity in place, makes subjects prefer the ambiguous bet over the objective one, reversing the prior results. |
| Keywords: | Uncertainty aversion, Probabilistic sophistication, Sources of ambiguity, Ellsberg paradox |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05012232 |
| By: | Aase, Knut K. (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | We consider optimal risk sharing where agents have preferences represented by translation invariant recursive utility. The dynamics in continuous time is driven by diffusion processes. The model has some appealing features compared to the scale invariant version. First, the model allows for heterogenous agents, where optimal risk sharing can be addressed. Second, a new endogenous variable allows for a variety of results, not possible in the standard model. The model allows for a new look at the mutuality principle. We also endow the model with a stock market and derive a consumption based capital asset pricing model. |
| Keywords: | Optimal risk sharing; the mutuality principle; recursive utility; CCAPM; the stochastic maximum principle |
| JEL: | D51 D53 D90 E21 G10 G12 |
| Date: | 2025–05–12 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:nhhfms:2025_016 |
| By: | Pawel‚ Doligalski (Group for Research in Applied Economics (GRAPE); Bristol University); Piotr Dworczak (Northwestern University; Group for Research in Applied Economics (GRAPE)); Mohammad Akbarpour (Stanford University); Scott Duke Kominers (Harvard Business School Harvard University; Harvard Business Becker Friedman Institute for Research in Economics University of Chicago; Department of Economics Harvard University) |
| Abstract: | Policymakers often intervene in goods markets to effect redistribution---for example, via price controls, differential taxation, or in-kind transfers. We investigate the optimality of such policies alongside the (optimally-designed) income tax. In our framework, agents possess private information about their ability to generate income and consumption preferences, and a planner maximizes a social welfare function subject to resource constraints. We uncover a generalization of the Atkinson-Stiglitz theorem by showing that goods markets should be undistorted if (i) individual utility functions feature no income effects, (ii) redistributive preferences depend only on agents’ ability, and (iii) there is no statistical correlation between ability and taste for goods. We also show, however, that the conclusion of the Atkinson-Stiglitz theorem fails if any of the three assumptions is relaxed. In a special case of our model with linear utilities, binary ability, and continuous willingness to pay for a single good, we characterize the globally optimal mechanism and show that it may feature means-tested consumption subsidies, in-kind transfers, and differential commodity taxation. |
| Keywords: | membership, allocative externalities, pricing tiers, rationing |
| JEL: | D47 D82 H21 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:fme:wpaper:103 |
| By: | Elvio Accinelli (Facultad de Economia, Universidad Autonoma de San Luís Potosí, México); Atefeh Afsar (Mathematics Department, Allen University, Columbia, SC, United States); Filipe Martins (University of Coimbra, CeBER and Faculty of Economics); José Martins (LIAAD INESC TEC, Escola Superior de Tecnologia e Gestão, Politecnico de Leiria); Bruno Oliveira (LIAAD INESC TEC, Faculdade de Ciências da Nutrição e Alimentação, Universidade do Porto); Alberto A. Pinto (LIAAD–INESC TEC, Departmento de Matemática, Faculdade de Ciências, Universidade do Porto); Luis Quintas (Universidad de La Punta, San Luis, Argentina) |
| Abstract: | Baliga and Maskin introduced a model of contributions for the provisions of public goods such as contributing for the reduction of air pollution. In this work we consider an extended version of Baliga and Maskin's model with a parameter a which is the elasticity of the benefit function, and with heterogeneous agents, each with their own preferences for the good. For this generalized version of the model, we consider the formation of stable coalitions which are absorbing states of a bargaining Markov chain, where agents join or leave coalitions according to their cooperation and free-riding incentives. We show that there is a stable high coalition consisting of the set of agents most preferring/valuing the public good. The increase of the elasticity parameter a increases the size of the stable high coalition that changes from a single member (called the competitive coalition as appearing in Baliga and Maskin's paper) to the grand coalition involving all agents. However, the utility of members of the stable coalition can be very small when compared to the utility of the free-riders, rendering the formation of stable coalitions difficult. We show that a variant of the coalition folk theorem holds, meaning that member heterogeneity will tend to decrease the size of stable coalitions. We show that the formation of stable coalitions is subject to the paradox of cooperation, since even when stable coalitions are large and free-riders have not very low preferences for the public good, the utility of the stable coalition may still be low when compared to the full cooperation scenario of the grand coalition. However, the paradox does not hold when the free-riders have a very low preference for the public good, which also facilitates the spontaneous formation of stable coalitions, or when there are no free-riders and the grand coalition is stable, which is always the case when the elasticity a is large enough. |
| Keywords: | public and common goods, free-riding, coalitions, stability, Barrett's paradox of cooperation, Markov chains |
| JEL: | C7 D7 H4 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:gmf:papers:2025-03 |
| By: | Arthur Jacobs (Ghent University) |
| Abstract: | I evaluate the link between automation and the rise in top income concentration when inequality matters for macro. The novel mechanism is that automation redistributes income towards high-wealth households who save more, which lowers the interest rate and incites firms to automate more. To operationalize this, I build a tractable heterogeneous-agent model (1) with wealth in the utility function as a luxury good, and (2) a firm-side choice on automation. I find that introducing realistic savings rate heterogeneity largely eliminates the need for ad hoc technology shifts. Rather, automation is the outcome of increased top income concentration, not just its driver. |
| Keywords: | automation, wealth inequality, capitalist spirit, task-based production, heterogeneous-agent |
| JEL: | E25 J23 O33 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:nbb:reswpp:202505-475 |
| By: | Cole Wittbrodt |
| Abstract: | Search and matching increasingly takes place on online platforms. These platforms have elements of centralized and decentralized matching; platforms can alter the search process for its users, but are unable to eliminate search frictions entirely. I study a model where platforms can change the distribution of potential partners that an agent searches over and characterize search equilibria on platforms. When agents possess private information about their match characteristics and the platform designer acts as a profit maximizing monopolist, I characterize the optimal platform. If match characteristics are complementary and utility is transferable, I show that the solution to this screening problem is efficient, despite the presence of hidden information and market power. Matching under the optimal platform is perfectly assortative -- there is no equilibrium mismatch. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.00205 |
| By: | Olivier J Blanchard (Peterson Institute for International Economics) |
| Abstract: | This year marks the 40th anniversary of the NBER Macro Annual Conference, founded in 1986. This paper reviews the evolution of mainstream macroeconomics since then. It presents Blanchard's views, informed by a survey of a number of researchers who have made important contributions to the field. He develops two main arguments. The first is that, starting from strikingly different positions, there has been substantial convergence, in terms of methodology, architecture, and main mechanisms. On methodology: Explicit micro foundations, explicit treatment of distortions, with, at the same time, an increased willingness to deviate from rational expectations, neoclassical utility, and profit maximization. On architecture: The wide acceptance of nominal rigidities as an essential distortion, although with mixed feelings. On mechanisms: The wide nature of the shocks to both the demand and the supply side. The second argument is that this convergence has been, for the most part, good convergence, i.e., the creation of a generally accepted conceptual and analytical structure, a core to which additional distortions can be added, allowing for discussions and integration of new ideas and evidence, rather than fights about basic methodology. Not everything is right however, with too much emphasis on general equilibrium implications from the start rather than, first, on partial equilibrium analysis of the phenomenon at hand. The appendix to the paper gives a sample of the views of the members of the survey on each of these arguments. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:iie:wpaper:wp25-8 |
| By: | Maćkowiak, Bartosz; Wiederholt, Mirko |
| Abstract: | We introduce an information provision experiment into a standard dynamic rational inattention model. We derive analytical results about how the treatment effect varies with characteristics of the environment and the individual. We use these results to discuss findings in the empirical literature on information provision experiments that can be explained by rational inattention of survey respondents and what this interpretation implies about behavior outside the survey. JEL Classification: D8, D9, E7 |
| Keywords: | information provision experiment, randomized control trial, rational inattention |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:ecb:ecbwps:20253054 |
| By: | Wang, Yuton; Guo, Jingyuan; Deng, Kent |
| Abstract: | Since Kenneth Pomeranz’s Great Divergence that was published in 2000, the scholarly debate has been focused on when the divergence was likely to begin. But a lack of real data for the Pomeranz framework has been noticeable. For our purpose, real data are imperative. The primary-source data this study uses are from the first large-scale modern survey of the rural economy in China in the 1920s and 30s to establish correlations between inputs, outputs and living standards in China’s rural sector. This study views China’s traditional growth trajectory continuing from the Qing to troubled times of the 1920s and 1930s despite considerable negative externalities from a regime change. The present view is that given that the rural economy managed to hang on during the Republican Period despite many disadvantages Qing China would have performed at least at the 1920s-30s’ level. Our findings indicate that rural population did indeed eat quite well during the politically troubled time, supporting Pomeranz’s pathbreaking comparison of utility functions between China’s Yangzi Delta and Western Europe. Secondly, food consumption proved incentives for improvement in labour productivity. Thirdly, China’s peasants were rational operators to maximise their returns. Fourthly, China’s highyield farming depended on land and labour inputs along a production probability frontier, which explains the root cause of the Great Divergence. Finally, there was a ‘little divergence’ inside China which was dictated by rice production, which justifies the Yangzi Delta as the best scenario. |
| Keywords: | Great Divergence; little divergence; primary-source data; inputs and outputs; living standards |
| JEL: | N35 N55 C51 |
| Date: | 2023–09–01 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:120277 |