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on Utility Models and Prospect Theory |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic, neuroscience-based theory of utility and disutility, replacing the static scalar utility functions of classical economics with a biologically grounded, mathematically rigorous framework. Drawing from molecular, cellular, systems, and computational neuroscience, we model subjective wellbeing as a neurodynamic process governed by differential equations, oscillatory systems, stochastic fluctuations, and quantum probability. The brain—containing roughly 100 billion neurons and 100 trillion synapses—emerges as the fundamental organ of economic valuation, with synaptic plasticity and circuit feedback shaping how pleasure, fatigue, and effort evolve over time. We present nine core equations that capture the temporal, spatial, and probabilistic structure of hedonic experience, integrating economic constraints such as PC=wL. These models reveal utility as a lived, adaptive, and embodied process, sensitive to consumption, labor, attention, and expectation. The framework offers a unified theory of welfare rooted in neurobiological complexity, enabling a redefinition of human flourishing through the combined lenses of economics and brain science. |
| Date: | 2025–05–16 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:753 |
| 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:journl:halshs-05053424 |
| By: | Biais, Bruno; Gersbach, Hans; Rochet, Jean-Charles; von Thadden, Ernst-Ludwig; Villeneuve, Stéphane |
| Abstract: | We analyze dynamic capital allocation and risk sharing between a principal and many agents, who privately observe their output. The state variables of the mechanism design problem are aggregate capital and the distribution of continuation utilities across agents. This gives rise to a Bellman equation in an infinite dimensional space, which we solve with mean-field techniques. We fully characterize the optimal mechanism and show that the level of risk agents must be exposed to for incentive reasons is decreasing in their initial outside utility. We extend classical welfare theorems by showing that any incentive- constrained optimal allocation can be implemented as an equilibrium allocation, with appropriate money issuance and wealth taxation by the principal. |
| Date: | 2025–05–22 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:130553 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a continuous-time mean field game model of capital accumulation with heterogeneous agents facing idiosyncratic stochastic productivity. Agents optimize infinite-horizon consumption under linear production and quadratic utility. The model yields a coupled Hamilton-Jacobi-Bellman and Fokker-Planck system, whose stationary solution ex hibits a Pareto-tailed wealth distribution. We derive the Pareto exponent analytically and show it depends on productivity and volatility. Numerical simulations confirm that realistic parameter values generate Gini coeffcients exceeding 0.7, consistent with empirical inequality. We evaluate the effectiveness of wealth taxation, consumption subsidies, and productivity equalization, finding these policies have limited long-run impact. Inequal ity emerges as a structural property of decentralized optimization under uncertainty, offering a micro-founded explanation for persistent wealth Concentration in capitalist economies. |
| Keywords: | Mean field games, wealth inequality, capital accumulation, Pareto distribution, stochastic dynamics, policy robustness |
| Date: | 2025–05–15 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:758 |
| By: | Tomohito Aoyama; Nobuyuki Hanaki |
| Abstract: | The random incentive system (RIS) is a standard incentive scheme used to elicit preferences in economic experiments. However, it has been speculated that RIS may distort observed preferences. We examine the performance of RIS under ambiguity with two sets of experiments, our own and another replicating the main treatments of Baillon et al. (2022a). Contrary to Baillon et al. (2022a), who report a significantly lower proportion of participants revealing strict ambiguity aversion in the treatment with RIS than the one without, we do not find such evidence either in our own or in replication of Baillon et al. (2022a). |
| Date: | 2024–03 |
| URL: | https://d.repec.org/n?u=RePEc:dpr:wpaper:1236r |
| By: | Ek, Simon (IFAU - Institute for Evaluation of Labour Market and Education Policy) |
| Abstract: | Are workers with poor outside opportunities less responsive and more susceptible to negative demand shifts in routine occupations? To answer this, I create and estimate an occupation specialization index (OSI) using Swedish register data and machine Learning tools. It measures the expected utility difference between a worker’s occupation and his best outside option. This determines the loss he is willing to tolerate to avoid switching. Low-OSI generalists disproportionately left routine work. Their future wage growth was comparable to similar workers initially in non-routine occupations. By contrast, routine specialists largely stayed put and experienced lower wage growth than generalists and non-routine specialists. |
| Keywords: | Multidimensional skills; Occupational structure changes |
| JEL: | J23 J24 J31 J62 |
| Date: | 2025–05–26 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:ifauwp:2025_007 |
| By: | Cappelen, Alexander W. (Dept. of Economics, Norwegian School of Economics and Business Administration); Sørensen, Erik Ø. (Dept. of Economics, Norwegian School of Economics and Business Administration); Tungodden, Bertil (Dept. of Economics, Norwegian School of Economics and Business Administration); Xu, Xiaogeng (Dept. of Finance and Economics, Hanken School of Economics) |
| Abstract: | Using a large, probability-based online panel representative of the general population in Norway, we examine how varying delays in the revelation of uncertainty affect risk-taking on behalf of others. We find a precisely estimated null effect of revelation delay on the average proportion choosing a lottery over a safe alternative. A hierarchical Bayesian model of rank-dependent utility also reveals no differences in underlying decision processes across conditions. However, we do observe a paternalistic tendency: participants place greater weight on their own risk preferences than on those they believe others to hold. |
| Keywords: | Risk-taking; decision-making; uncertainty |
| JEL: | C91 D63 D81 |
| Date: | 2025–05–23 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:nhheco:2025_013 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic model of power accumulation and inequality using the framework of mean field games. Agents optimize intertemporally over consumption while accumulating power as a capital stock, subject to idiosyncratic productivity shocks. Power yields direct utility and enhances future accumulation. In equilibrium, the joint distribution of power and productivity evolves endogenously via a coupled Hamilton-Jacobi-Bellman and Fokker-Planck system. We prove that - even absent initial heterogeneity-persistent inequality and elite dominance emerge as stable outcomes. The stationary distribution exhibits fat tails and high Gini coefficients, consistent with empirical observations of power concentration in historical empires and modern regimes. The model offers a structural explanation for the recurrent emergence of dominant elites under decentralized, rational decision-making. |
| Keywords: | power accumulation, inequality, mean field games, elite dominance, stochastic dynamics |
| Date: | 2025–05–15 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:759 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic, multi-country model in which governments strategically set import tariffs to fund national defense, and representative agents derive utility from consumption, capital, foreign asset holdings, and publicly financed military strength. The model embeds mercantilist-nationalist preferences within a linear-quadratic-Gaussian (LQG) framework, allowing closed-form solutions for optimal consumption, savings, and trade behavior. We extend the model to a mean field game, where each government optimizes its tariff policy in response to the aggregate tariff behavior of all other countries. The equilibrium is characterized by a Hamilton-Jacobi-Bellman-Fokker-Planck system and features endogenously determined global interest rates, cross-country capital flows, and securitized trade patterns. Simulations reveal a structural mercantilist trap: globally depressed interest rates, strategic reserve ac cumulation, and persistent trade imbalances. The model explains how decentralized, rational policy behavior under sovereignty and security concerns gives rise to systemic instability and geopolitical fragmentation in today's global economic order. |
| Keywords: | Mercantilism, Strategic Trade Policy, Mean Field Games, National Defense, Foreign Asset Accumulation |
| Date: | 2025–05–03 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:760 |
| By: | Tsoulfidis, Lefteris |
| Abstract: | Smith's theory of value and distribution, which emphasizes labor time as the determinant of prices, has been widely misunderstood. Ricardo misinterpreted it as relevant only to primitive societies, while Marx mistakenly aligned it with his own labor theory of value. In reality, Smith’s perspective oscillates between a labor-based and a labor-commanded approach to relative prices, intended for modern economies. Neoclassical economists further distorted Smith’s views by incorporating utility theory. Moreover, while Smith is often linked to the theory of a falling rate of profit due to competition, he actually attributed it to rising capital intensity. Contrary to the belief that Smith was a staunch advocate of free markets, he supported reasonable government intervention. |
| Keywords: | Labor theory of value, falling rate of profit, labor commanded, capital intensity |
| JEL: | B00 B31 B51 N00 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:124796 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic mean field game model to explain the emergence of heavy-tailed city size distributions and persistent urban inequality. Each city optimizes intertemporal consumption and investment in infrastructure to maximize utility from both consumption and population scale. City size follows a stochastic process with investment-driven drift, while productivity evolves as a mean-reverting diffusion. We derive the equilibrium using the Lasry–Lions Master Equation and simulate the resulting stationary distribution. The model generates high Gini coefficients and Pareto-like upper tails, consistent with Zipf’s law and Gibrat’s law. These patterns arise endogenously through capital accumulation, productivity shocks, and scale feedbacks, offering a unified framework to understand urban size inequality. |
| Keywords: | City size distribution, Zipf's law, Gibrat's law, Mean field games, Urban inequality, Capital accumulation |
| Date: | 2025–05–15 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:757 |
| By: | Sumedh Gupte; Prashanth L. A.; Sanjay P. Bhat |
| Abstract: | We consider the problems of estimation and optimization of two popular convex risk mea- sures: utility-based shortfall risk (UBSR) and Optimized Certainty Equivalent (OCE) risk. We extend these risk measures to cover possibly unbounded random variables. We cover prominent risk measures like the entropic risk, expectile risk, monotone mean-variance risk, Value-at-Risk, and Conditional Value-at-Risk as few special cases of either the UBSR or the OCE risk. In the context of estimation, we derive non-asymptotic bounds on the mean absolute error (MAE) and mean-squared error (MSE) of the classical sample average approximation (SAA) estimators of both, the UBSR and the OCE. Next, in the context of optimization, we derive expressions for the UBSR gradient and the OCE gradient under a smooth parameterization. Utilizing these expres- sions, we propose gradient estimators for both, the UBSR and the OCE. We use the SAA estimator of UBSR in both these gradient estimators, and derive non-asymptotic bounds on MAE and MSE for the proposed gradient estimation schemes. We incorporate the aforementioned gradient estima- tors into a stochastic gradient (SG) algorithm for optimization. Finally, we derive non-asymptotic bounds that quantify the rate of convergence of our SG algorithm for the optimization of the UBSR and the OCE risk measure |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.01101 |