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on Utility Models and Prospect Theory |
| By: | Maxwell Rosenthal |
| Abstract: | This paper proposes a fully prior-free model of experimentation in which the decision maker observes the entire distribution of signals generated by a known experiment under an unknown distribution of the state of the world. One experiment is robustly more informative than another if the decision maker's maxmin expected utility after observing the output of the former is always at least her maxmin expected utility after observing the latter. We show that this ranking holds if and only if the less informative experiment is a linear transformation of the more informative experiment; equivalently, the null space of the more informative experiment is a subset of the null space of the less informative experiment. Our criterion is implied by Blackwell's order but does not imply it, and we show by example that our ranking admits strictly more comparable pairs of experiments than the classical ranking. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.08709 |
| By: | Natalie Collina; Surbhi Goel; Aaron Roth; Emily Ryu; Mirah Shi |
| Abstract: | Aligning AI systems with human values remains a fundamental challenge, but does our inability to create perfectly aligned models preclude obtaining the benefits of alignment? We study a strategic setting where a human user interacts with multiple differently misaligned AI agents, none of which are individually well-aligned. Our key insight is that when the users utility lies approximately within the convex hull of the agents utilities, a condition that becomes easier to satisfy as model diversity increases, strategic competition can yield outcomes comparable to interacting with a perfectly aligned model. We model this as a multi-leader Stackelberg game, extending Bayesian persuasion to multi-round conversations between differently informed parties, and prove three results: (1) when perfect alignment would allow the user to learn her Bayes-optimal action, she can also do so in all equilibria under the convex hull condition (2) under weaker assumptions requiring only approximate utility learning, a non-strategic user employing quantal response achieves near-optimal utility in all equilibria and (3) when the user selects the best single AI after an evaluation period, equilibrium guarantees remain near-optimal without further distributional assumptions. We complement the theory with two sets of experiments. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.15090 |
| By: | Dejian Tian; Weidong Tian; Jianjun Zhou; Zimu Zhu |
| Abstract: | We study optimal portfolio choice under Epstein-Zin recursive utility in the presence of general leverage constraints. We first establish that the optimal value function is the unique viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, by developing a new dynamic programming principle under constraints. We further demonstrate that the value function admits smoothness and characterize the optimal consumption and investment strategies. In addition, we derive explicit solutions for the optimal strategy and explicitly delineate the constrained and unconstrained regions in several special cases of the leverage constraint. Finally, we conduct a comparative analysis, highlighting the differences relative to the classical time-separable preferences and to the setting without leverage constraints. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.21929 |
| By: | Martyna Kobus; Rados{\l}aw Kurek; Thomas Parker |
| Abstract: | Strong empirical evidence from laboratory experiments, and more recently from population surveys, shows that individuals, when evaluating their situations, pay attention to whether they experience gains or losses, with losses weighing more heavily than gains. The electorate's loss aversion, in turn, influences politicians' choices. We propose a new framework for welfare analysis of policy outcomes that, in addition to the traditional focus on post-policy incomes, also accounts for individuals' gains and losses resulting from policies. We develop several bivariate stochastic dominance criteria for ranking policy outcomes that are sensitive to features of the joint distribution of individuals' income changes and absolute incomes. The main social objective assumes that individuals are loss averse with respect to income gains and losses, inequality averse with respect to absolute incomes, and hold varying preferences regarding the association between incomes and income changes. We translate these and other preferences into functional inequalities that can be tested using sample data. The concepts and methods are illustrated using data from an income support experiment conducted in Connecticut. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.09590 |
| By: | Enrico G. De Giorgi (University of St. Gallen - SEPS: Economics and Political Sciences; Swiss Finance Institute); Thierry Post (Graduate School of Business of Nazarbayev University); Askhat Omar (Nazarbayev University - Graduate School of Business) |
| Abstract: | We present experimental evidence of systematic decision errors in dynamic portfolio choice. Participants created contingency plans in a lattice model. When returns were independent and identically distributed, most plans were near-optimal for plausible risk preferences. However, under dynamic probabilities, most plans were inefficient, even by First-degree Stochastic Dominance. Allocations showed a lack of sensitivity to probability shifts, consistent with myopic loss aversion. Decision quality improved when participants compared their original plan to precomputed optimal plans. Results highlight the importance of problem framing in dynamic choice and support a libertarian paternalistic approach to choice architecture design. |
| Keywords: | Dynamic portfolio choice, choice experiments, myopic loss aversion |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:chf:rpseri:rp2578 |
| By: | Pauline Corblet; Jeremy T. Fox; Alfred Galichon |
| Abstract: | We introduce a model of dynamic matching with transferable utility, extending the static model of Shapley and Shubik (1971). Forward-looking agents have individual states that evolve with current matches. Each period, a matching market with market-clearing prices takes place. We prove the existence of an equilibrium with time-varying distributions of agent types and show it is the solution to a social planner’s problem. We also prove that a stationary equilibrium exists. We introduce econometric shocks to account for unobserved heterogeneity in match formation. We propose two algorithms to compute a stationary equilibrium. We adapt both algorithms for estimation. We estimate a model of accumulation of job-specific human capital using data on Swedish engineers. |
| JEL: | C1 C78 J20 L10 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:34352 |
| By: | Nathalie Gimenes; Tonghui Qi; Sorawoot Srisuma |
| Abstract: | How sellers choose reserve prices is central to auction theory, and the optimal reserve price depends on the seller's risk attitude. Numerous studies have found that observed reserve prices lie below the optimal level implied by risk-neutral sellers, while the theoretical literature suggests that risk-averse sellers can rationalize these empirical findings. In this paper, we develop an econometric model of ascending auctions with a risk-averse seller under independent private values. We provide primitive conditions for the identification of the Arrow-Pratt measures of risk aversion and an estimator for these measures that is consistent and converges in distribution to a normal distribution at the parametric rate under standard regularity conditions. A Monte Carlo study demonstrates good finite-sample performance of the estimator, and we illustrate the approach using data from foreclosure real estate auctions in S\~{a}o Paulo. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.19945 |
| By: | Marcin Dziubi\'nski; Sanjeev Goyal; Junjie Zhou |
| Abstract: | We study a two-player model of conflict with multiple battlefields -- the novel element is that each of the players has their own network of spillovers so that resources allocated to one battle can be utilized in winning neighboring battles. There exists a unique equilibrium in which the relative probability of a player winning a battle is the product of the ratio of the centrality of the battlefield in the two respective competing networks and the ratio of the relative cost of efforts of the two players. We study the design of networks and characterize networks that maximize total efforts and maximize total utility. Finally, we characterize the equilibrium of a game in which players choose both networks and efforts in the battles. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.11452 |
| By: | Christian Laudag\'e; Felix-Benedikt Liebrich |
| Abstract: | Motivated by recent work on monotone additive statistics and questions regarding optimal risk sharing for return-based risk measures, we investigate the existence, structure, and applications of Meyer risk measures. Those are monetary risk measures consistent with fractional stochastic orders suggested by Meyer (1977a, b) as refinement of second-order stochastic dominance (SSD). These so-called $v$-SD orders are based on a threshold utility function $v$. The test utilities defining the associated order are those at least as risk averse in absolute terms as $v$. The generality of $v$ allows to subsume SSD and other examples from the literature. The structure of risk measures respecting the $v$-SD order is clarified by two types of representations. The existence of nontrivial examples is more subtle: for many choices of $v$ outside the exponential (CARA) class, they do not exist. Additional properties like convexity or positive homogeneity further restrict admissible examples, even within the CARA class. We present impossibility theorems that demonstrate a deeper link between the axiomatic structure of monetary risk measures and SSD than previously acknowledged. The study concludes with two applications: portfolio optimisation under a Meyer risk measure as objective, and risk assessment of financial time series data. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.24747 |
| By: | Xinqiao Xie; Jonathan Yu-Meng Li |
| Abstract: | Conditional risk minimization arises in high-stakes decisions where risk must be assessed in light of side information, such as stressed economic conditions, specific customer profiles, or other contextual covariates. Constructing reliable conditional distributions from limited data is notoriously difficult, motivating a series of optimal-transport-based proposals that address this uncertainty in a distributionally robust manner. Yet these approaches remain fragmented, each constrained by its own limitations: some rely on point estimates or restrictive structural assumptions, others apply only to narrow classes of risk measures, and their structural connections are unclear. We introduce a universal framework for distributionally robust conditional risk minimization, built on a novel union-ball formulation in optimal transport. This framework offers three key advantages: interpretability, by subsuming existing methods as special cases and revealing their deep structural links; tractability, by yielding convex reformulations for virtually all major risk functionals studied in the literature; and scalability, by supporting cutting-plane algorithms for large-scale conditional risk problems. Applications to portfolio optimization with rank-dependent expected utility highlight the practical effectiveness of the framework, with conditional models converging to optimal solutions where unconditional ones clearly do not. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.23128 |
| By: | Lammers, Wouter; Puimège, Eva; Pattyn, Valérie; Van de Walle, Steven |
| Abstract: | Civil servants often have to make decisions supported by uncertain information, yet it remains unclear how they prioritize different types of uncertainty. We distinguish shallow, quantified uncertainty from deep, ambiguous uncertainty. Ambiguity aversion suggests that shallow uncertainty information will distract attention away from deep uncertainty information, potentially leading to overconfident decisions. This eye-tracking study investigates how civil servants read and use deep and shallow uncertainty information regarding a procurement decision. Contrary to expectations, we find that shallow uncertainty does not distract from deep uncertainty but boosts concentration towards it. The presence of shallow uncertainty impacts decision-making but not decision confidence. |
| Date: | 2025–10–09 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:cpyra_v1 |
| By: | Hai Ha Pham (EM Normandie); Ngoc-Sang Pham (EM Normandie) |
| Abstract: | We investigate the effects of wariness (defined as individuals' concern for their minimum utility over time) on poverty traps and equilibrium multiplicity in an overlapping generations (OLG) model. We explore conditions under which (i) wariness amplifies or mitigates the likelihood of poverty traps in the economy and (ii) it gives rise to multiple intertemporal equilibria. Furthermore, we conduct comparative statics to characterize these effects and to examine how the interplay between wariness, productivity, and factor substitutability influences the dynamics of the economy. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.14418 |
| By: | Onil Boussim |
| Abstract: | In difference-in-differences (DiD) settings with categorical outcomes, treatment effects often operate on both total quantities (e.g., voter turnout) and category shares (e.g., vote distribution across parties). In this context, linear DiD models can be problematic: they suffer from scale dependence, may produce negative counterfactual quantities, and are inconsistent with discrete choice theory. We propose compositional DiD (CoDiD), a new method that identifies counterfactual categorical quantities, and thus total levels and shares, under a parallel growths assumption. The assumption states that, absent treatment, each category's size grows or shrinks at the same proportional rate in treated and control groups. In a random utility framework, we show that this implies parallel evolution of relative preferences between any pair of categories. Analytically, we show that it also means the shares are reallocated in the same way in both groups in the absence of treatment. Finally, geometrically, it corresponds to parallel trajectories (or movements) of probability mass functions of the two groups in the probability simplex under Aitchison geometry. We extend CoDiD to i) derive bounds under relaxed assumptions, ii) handle staggered adoption, and iii) propose a synthetic DiD analog. We illustrate the method's empirical relevance through two applications: first, we examine how early voting reforms affect voter choice in U.S. presidential elections; second, we analyze how the Regional Greenhouse Gas Initiative (RGGI) affected the composition of electricity generation across sources such as coal, natural gas, nuclear, and renewables. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.11659 |
| By: | Masaaki Fujii (Graduate School of Economics, The University of Tokyo) |
| Abstract: | In this work, we combine the mean-fi eld game theory with the classical idea of binomial tree framework, pioneered by Sharpe and Cox, Ross & Rubinstein, to solve the equilibrium price formation problem for the stock. For agents with exponential utilities and recursive utilities of exponential type, we prove the existence of a unique mean- field equilibrium and derive an explicit formula for equilibrium transition probabilities of the stock price by restricting its trajectories onto a binomial tree. The agents are subject to stochastic terminal liabilities and incremental endowments, both of which are dependent on unhedgeable common and idiosyncratic factors, in addition to the stock price path. Finally, we provide numerical examples to illustrate the qualitative effects of these components on the equilibrium price distribution. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:cfi:fseres:cf606 |
| By: | Mohamed Bahlali (Aix-Marseille Univ., CNRS, AMSE, Marseille, France); Raouf Boucekkine (Aix-Marseille Univ., CNRS, AMSE, Marseille, France); Quentin Petit (EDF & FiME Lab, Paris, France) |
| Abstract: | We propose a mean-field game (MFG) set-up to study the dynamics of spatial agglomeration in a continuous space-time framework where trade across locations may follow a broad class of static gravity models. Forward-looking intertemporal utility-maximizing agents work and migrate in a twodimensional geography and face idiosyncratic shocks. Equilibrium wages and prices depend on their common distribution and adjust statically according to the underlying trade model. We first prove existence and uniqueness of the static trade equilibrium. We then prove existence of dynamic equilibria. In the case of Krugman (1996)'s racetrack economy, we obtain closed-form solutions for small sinusoidal perturbations around the steady state, and we identify the sets of parameters that lead to agglomeration or dispersion. We exploit the MFG structure of the model to explicitly quantify how uncertainty and forward-looking expectations contribute to agglomeration and dispersion. In particular, we show that, regardless of the static trade model, forward-looking expectations always promote agglomeration, but cannot reverse the dominant pattern that would arise under myopic behavior. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:aim:wpaimx:2517 |
| By: | Masaaki Fujii |
| Abstract: | In this work, we combine the mean-field game theory with the classical idea of binomial tree framework, pioneered by Sharpe and Cox, Ross & Rubinstein, to solve the equilibrium price formation problem for the stock. For agents with exponential utilities and recursive utilities of exponential type, we prove the existence of a unique mean-field equilibrium and derive an explicit formula for equilibrium transition probabilities of the stock price by restricting its trajectories onto a binomial tree. The agents are subject to stochastic terminal liabilities and incremental endowments, both of which are dependent on unhedgeable common and idiosyncratic factors, in addition to the stock price path. Finally, we provide numerical examples to illustrate the qualitative effects of these components on the equilibrium price distribution. |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2510.11261 |
| By: | Yun Zhao; Harry Zheng |
| Abstract: | We propose an approach to applying neural networks on linear parabolic variational inequalities. We use loss functions that directly incorporate the variational inequality on the whole domain to bypass the need to determine the stopping region in advance and prove the existence of neural networks whose losses converge to zero. We also prove the functional convergence in the Sobolev space. We then apply our approach to solving an optimal investment and stopping problem in finance. By leveraging duality, we convert the nonlinear HJB-type variational inequality of the primal problem into a linear variational inequality of the dual problem and prove the convergence of the primal value function from the dual neural network solution, an outcome made possible by our Sobolev norm analysis. We illustrate the versatility and accuracy of our method with numerical examples for both power and non-HARA utilities as well as high-dimensional American put option pricing. Our results underscore the potential of neural networks for solving variational inequalities in optimal stopping and control problems. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.26535 |