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on Utility Models and Prospect Theory |
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Issue of 2025–09–01
thirteen papers chosen by |
| By: | Mononen, Lasse (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We characterize the empirical content of expected utility. We show that the empirical content of the expected utility theory is contained in completeness, transitivity, and strong independence axioms. However, under commonly used weaker forms of independence axiom, the continuity adds empirical content in the expected utility theory. This formalizes and makes exact the ubiquitous claim that the continuity axiom is a technical axiom without empirical content in the expected utility theory. |
| Date: | 2025–08–15 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:737 |
| By: | Mononen, Lasse (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We reconsider the foundations of expected utility without assuming the linearity of the independence axiom. We consider a decision-maker who cancels out common outcomes when comparing a pair of lotteries with the same probability tree. We show that if the decision-maker is consistent with first-order stochastic dominance or topological continuity in weak convergence, then the decision-maker is an expected utility maximizer. This offers a simple method to differentiate behavior between prospect theory, canceling out common outcomes in pairwise comparisons, and cumulative prospect theory, satisfying first-order stochastic dominance. Additionally, this offers a novel method to test technical continuity assumptions based on their behavioral content that rules out, e.g., prospect theory. |
| Keywords: | Expected utility, branch cancellation, first-order stochastic dominance, testing axioms, prospect theory, cumulative prospect theory |
| Date: | 2025–08–14 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:728 |
| By: | Mononen, Lasse (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | Models of choice under uncertainty study choice behavior when outcomes depend on the realized state of the world. The typical assumption is that utilities of outcomes do not depend on the realized state and are state independent. Without this simplifying assumption, it is difficult to separately identify utilities and beliefs. This paper provides novel general foundations for models with state dependent utilities: once we depart from expected utility, it is often possible to uniquely identify utilities and beliefs. Specifically, we show that with general models of non-expected utility under ambiguity we have complete identification of utilities and probabilities under full-dimensional uncertainty. Additionally, we offer novel axiomatizations for state dependent dual-self variational expected utility and dual-self expected utility. |
| Keywords: | State dependent utility, belief identification, ambiguity, multiple priors, dual-self expected utility |
| Date: | 2025–08–15 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:738 |
| By: | Beißner, Patrick (Center for Mathematical Economics, Bielefeld University); Werner, Jan (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | The analysis of optimal risk sharing has been thus far largely restricted to non-expected utility models with concave utility functions, where concavity is an expression of ambiguity aversion and/or risk aversion. This paper extends the analysis to $\alpha$-maxmin expected utility, Choquet expected utility, and Cumulative Prospect Theory, which accommodate ambiguity seeking and risk seeking attitudes. We introduce a novel methodology of quasidifferential calculus of Demyanov and Rubinov (1986, 1992) and argue that it is particularly well-suited for the analysis of these three classes of utility functions which are neither concave nor differentiable. We provide characterizations of quasidifferentials of these utility functions, derive first-order conditions for Pareto optimal allocations under uncertainty, and analyze implications of these conditions for risk sharing with and without aggregate risk. |
| Keywords: | quasidifferential calculus, ambiguity, Pareto optimality, $\alpha$-MaxMin expected utility, Choquet expected utility, rank-dependent expected utility, Cumulative Prospect Theory |
| Date: | 2025–07–18 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:722 |
| By: | Mononen, Lasse (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | Complexity aversion is well-documented in choice under risk. One of the main behavioral effects of complexity aversion is the event-splitting effect. This captures the change in the value of a lottery from splitting a prize of the lottery into two separate prizes by halving the probability. We relax the independence axiom for the event-splitting effect. Under continuity assumptions, this characterizes a decision-maker that is either 1) an expected utility maximizer with an entropic cost of complexity or 2) a powerweighted expected utility maximizer that weights probabilities by a power function. Additionally, our model offers preference foundations for the logit random choice. |
| Date: | 2025–08–18 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:748 |
| By: | Patrick Lederer |
| Abstract: | Social decision schemes (SDSs) map the voters' preferences over multiple alternatives to a probability distribution over these alternatives. In a seminal result, Gibbard (1977) has characterized the set of SDSs that are strategyproof with respect to all utility functions and his result implies that all such SDSs are either unfair to the voters or alternatives, or they require a significant amount of randomization. To circumvent this negative result, we propose the notion of $U$-strategyproofness which postulates that only voters with a utility function in a predefined set $U$ cannot manipulate. We then analyze the tradeoff between $U$-strategyproofness and various decisiveness notions that restrict the amount of randomization of SDSs. In particular, we show that if the utility functions in the set $U$ value the best alternative much more than other alternatives, there are $U$-strategyproof SDSs that choose an alternative with probability $1$ whenever all but $k$ voters rank it first. On the negative side, we demonstrate that $U$-strategyproofness is incompatible with Condorcet-consistency if the set $U$ satisfies minimal symmetry conditions. Finally, we show that no ex post efficient and $U$-strategyproof SDS can be significantly more decisive than the uniform random dictatorship if the voters are close to indifferent between their two favorite alternatives. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.16195 |
| By: | Jiacheng Fan; Xue Dong He; Ruocheng Wu |
| Abstract: | We study a dynamic asset pricing problem in which a representative agent is ambiguous about the aggregate endowment growth rate and trades a risky stock, human capital, and a risk-free asset to maximize her preference value of consumption represented by the {\alpha}-maxmin expected utility model. This preference model is known to be dynamically inconsistent, so we consider intra-personal equilibrium strategies for the representative agent and define the market equilibrium as the one in which the strategy that clears the market is an intra-personal equilibrium. We prove the existence and uniqueness of the market equilibrium and show that the asset prices in the equilibrium are the same as in the case when the agent does not perceive any ambiguity but believes in a particular probabilistic model of the endowment process. We show that with reasonable parameter values, the more ambiguity the agent perceives or the more ambiguity-averse she is, the lower the risk-free rate, the higher the stock price, the higher the stock risk premium, and the lower the stock volatility. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.04093 |
| By: | Keinprecht, Michael |
| Abstract: | The growing inequalities around the world are becoming increasingly alarming making redistribution more relevant than ever. One reason why people may oppose redistribution is third party loss aversion. In a pre-registered online experiment with a within-subjects design, I show that redistribution decisions by third parties are affected by loss aversion. Overall, spectators are 7%-points less likely to redistribute from a status quo to an alternative if the alternative entails a loss for one person, even if inequality aversion, maximin preferences and efficiency concerns favor the alternative. This effect is stronger the higher the loss is compared to the gain and the higher the individual loss aversion of the spectator. The key contribution of the paper is to disentangle third party loss aversion from pure status quo bias, rank reversal aversion and other distributional preferences in multiple loss scenarios and to link it to individual loss aversion. |
| Keywords: | Third party loss aversion; loss aversion; redistribution; spectators; fairness |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:wiw:wus005:76570814 |
| By: | Kitamura, Kazuhito |
| Abstract: | This paper challenges traditional economics' reliance on Adam Smith's "invisible hand" and its assumption of equilibrium derived from nominal variables, arguing that this hinders economists' understanding of modern economies. It proposes "dynamic equilibrium, " where stability arises from interactions between agents' internal characteristics and external factors. A key equation derived from the paper is "R_t-ρ=n+D_a-(U_(θa)θ)/U_c". Its left-hand side, the discrepancy between asset return (R_t) and time preference rate (ρ), is balanced by two forces on the right-hand side: retaining capital within the economy (the marginal utility of assets compared to consumption) and promoting its diffusion and dilution (capital outflow (D_a) and population growth (n)). That suggests that if time preference is an inherent trait, economies with a lower time preference will have a funds surplus, but this will be partially offset by capital outflow or a weak asset preference, so the decline in the real interest rate will be limited, and vice varsa. The paper argues that while conventional economics has focused on the left-hand side of this equation, understanding the right-hand side is crucial. This mechanism will be able to pragmatically explain various modern economic phenomena through the immobilization of the relations between debtor and creditor even when agents are rational and markets are efficient : for example, long-term global imbalances, deflationary equilibrium in developed economies, and inequalities of income and assets and so on. Ultimately, the paper reinterprets modern economic disequilibrium as a result of rational agent behavior, offering insights for more effective macroeconomic policy. |
| Date: | 2025–07–28 |
| URL: | https://d.repec.org/n?u=RePEc:osf:socarx:3dqfg_v1 |
| By: | Costa-Font, Joan; Cowell, Frank |
| Abstract: | An individual’s inequality aversion (IA) is a central preference parameter that captures the welfare sacrifice from exposure to inequality. However, it is far from trivial how best to elicit IA estimates. Also, little is known about the behavioural determinants of IA and how they differ across domains such as income and health. Using representative surveys from England, this paper elicits comparable estimates of IA in the health and income domains using two alternative elicitation techniques: a direct trade-off and an indirect “imaginary-grandchild” approach that results from the choices between hypothetical lotteries. We make three distinct contributions to the literature. First, we show that IA systematically differs between income and health domains. Average estimates are around 0.8 for health IA and range from 0.8 to 1.5 for income IA. Second, we find that risk aversion and locus of control are central determinants of IA in both income and health domains. Finally, we present evidence suggesting that the distribution and comparison of IA vary depending on the elicitation method employed. |
| Keywords: | inequality aversion; income inequality aversion; health inequality aversion; imaginary grandchild; inequality and efficiency trade-offs; risk attitudes; locus of control |
| JEL: | H10 I18 |
| Date: | 2025–08–14 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:128734 |
| By: | Takashi Izumo |
| Abstract: | The St. Petersburg paradox presents a longstanding challenge in decision theory. It describes a game whose expected value is infinite, yet for which no rational finite stake can be determined. Traditional solutions introduce auxiliary assumptions, such as diminishing marginal utility, temporal discounting, or extended number systems. These methods often involve mathematical refinements that may not correspond to how people actually perceive or process numerical information. This paper explores an alternative approach based on a modified operation of addition defined over coarse partitions of the outcome space. In this model, exact numerical values are grouped into perceptual categories, and each value is replaced by a representative element of its group before being added. This method allows for a phenomenon where repeated additions eventually cease to affect the outcome, a behavior described as inertial stabilization. Although this is not intended as a definitive resolution of the paradox, the proposed framework offers a plausible way to represent how agents with limited cognitive precision might handle divergent reward structures. We demonstrate that the St. Petersburg series can become inert under this coarse addition for a suitably constructed partition. The approach may also have broader applications in behavioral modeling and the study of machine reasoning under perceptual limitations. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.12475 |
| By: | Daiya Mita (Nomura Asset Management Co. Ltd.); Taiga Saito (Graduate School of Economics, Hitotsubashi University); Akihiko Takahashi (Graduate School of Economics, The University of Tokyo) |
| Abstract: | For global multi-asset fund managers, reflecting their macroeconomic views in the prediction of expected interest rates across countries, exchange rates, and equity prices in a manner consistent with economic theory is challenging. The existing literature has yet to provide an established multi-currency model that is flexible enough to incorporate such views into the prediction of future asset price dynamics. To address this problem, this paper proposes a novel multi-currency incomplete market model in which agents in each country have logarithmic utility but differ in their time references and subjective beliefs, within a market equilibrium framework, namely, supply and demand equilibrium. With only a few exogenous inputs, such as each country’s output process and agents’ preference parameters, the model endogenously determines equilibrium interest rates, exchange rates, and stock prices, along with optimal consumption and portfolios. Thus, the model enables us to (i) flexibly incorporate cross-country differences in investors’ time preferences and macroeconomic outlooks, and (ii) examine how these differences affect equilibrium interest rates and asset prices, including stock prices and exchange rates. Moreover, by applying the particle filtering method within a state-space framework based on the two-country, two-currency version of the model to Japanese and U.S. market data (equity index futures, short-term interest rates, and the exchange rate), the model not only fits the observed dynamics of equity indices, short rates, and the exchange rate, but also effectively estimates the dynamics of home-country biases and latent economic factors, which can be utilized in making investment decisions in asset management practice. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:cfi:fseres:cf603 |
| By: | Hu Fu; Tao Lin |
| Abstract: | In non-truthful auctions such as first-price and all-pay auctions, the independent strategic behaviors of bidders, with the corresponding equilibrium notion -- Bayes Nash equilibria -- are notoriously difficult to characterize and can cause undesirable outcomes. An alternative approach to designing better auction systems is to coordinate the bidders: let a mediator make incentive-compatible recommendations of correlated bidding strategies to the bidders, namely, implementing a Bayes correlated equilibrium (BCE). The implementation of BCE, however, requires knowledge of the distribution of bidders' private valuations, which is often unavailable. We initiate the study of the sample complexity of learning Bayes correlated equilibria in non-truthful auctions. We prove that the BCEs in a large class of non-truthful auctions, including first-price and all-pay auctions, can be learned with a polynomial number $\tilde O(\frac{n}{\varepsilon^2})$ of samples from the bidders' value distributions. Our technique is a reduction to the problem of estimating bidders' expected utility from samples, combined with an analysis of the pseudo-dimension of the class of all monotone bidding strategies of bidders. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.02801 |