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on Utility Models and Prospect Theory |
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Issue of 2024‒04‒01
eighteen papers chosen by |
| By: | Thomas Dohmen; Georgios Gerasimou |
| Abstract: | We study if participants in a choice experiment learn to behave in ways that are closer to the predictions of ordinal and expected utility theory as they make decisions from the same menus repeatedly and without receiving feedback of any kind. We designed and implemented a non-forced-choice lab experiment with money lotteries and five repetitions per menu that aimed to test this hypothesis from many behavioural angles. In our data from 308 subjects in the UK and Germany, significantly more individuals were ordinal- and expected-utility maximizers in their last 15 than in their first 15 identical decision problems. Furthermore, around a quarter and a fifth of all subjects, respectively, decided in those modes throughout the experiment, with nearly half revealing non-trivial indifferences. A considerable overlap was found between those consistently rational individuals and the ones who satisfied core principles of random utility theory. Finally, in addition to finding that choice consistency is positively correlated with cognitive ability, we document that subjects who learned to maximize utility were more cognitively able than those who did not. We discuss potential implications of our analysis. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.16538&r=upt |
| By: | Phoebe Koundouri; Nikitas Pittis (University of Piraeus, Greece); Panagiotis Samartzis |
| Abstract: | Ellsberg-type choices (Ellsberg's paradox) are evidence against the Bayesian theory of Subjective Expected Utility Maximization (SEUM). These choices reflect a particular attitude of the decision maker (DM), namely Ambiguity Aversion (AA). There are two competing interpretations of AA. The first recognizes AA as rational behavior, while the second views AA as a manifestation of a psychological fallacy. This paper focuses on the second interpretation of AA and specifically discusses the most important psychological explanation of AA that has been proposed in the literature, namely Fox and Tversky's (1995) Comparative Ignorance Hypothesis (CIH). CIH holds that AA is mainly a "comparative effect" that occurs when DM feels that he is epistemically inferior for some events of interest compared to others (for which she believes to be epistemically superior). As a result, DM exhibits an aversion towards betting on the epistemically inferior events. The purpose of the paper is twofold: First, to provide a survey of the literature on CIH. Second, to propose a novel "Bayesian Training" (BT) procedure based on "counterfactual thinking". A decision maker who finds BT attractive is likely to move out of the state of comparative ignorance, thereby ceasing to exhibit AA and joining the Bayesian camp. |
| Keywords: | counterfactual priors, ambiguity, ellsberg paradox |
| JEL: | C44 D81 D83 D89 |
| URL: | http://d.repec.org/n?u=RePEc:aue:wpaper:2408&r=upt |
| By: | Alfred Galichon; Antoine Jacquet |
| Abstract: | Matching problems with linearly transferable utility (LTU) generalize the well-studied transferable utility (TU) case by relaxing the assumption that utility is transferred one-for-one within matched pairs. We show that LTU matching problems can be reframed as nonzero-sum games between two players, thus generalizing a result from von Neumann. The underlying linear programming structure of TU matching problems, however, is lost when moving to LTU. These results draw a new bridge between non-TU matching problems and the theory of bimatrix games, with consequences notably regarding the computation of stable outcomes. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.12200&r=upt |
| By: | Tim Leung; Matthew Lorig; Yoshihiro Shirai |
| Abstract: | This paper analyzes a problem of optimal static hedging using derivatives in incomplete markets. The investor is assumed to have a risk exposure to two underlying assets. The hedging instruments are vanilla options written on a single underlying asset. The hedging problem is formulated as a utility maximization problem whereby the form of the optimal static hedge is determined. Among our results, a semi-analytical solution for the optimizer is found through variational methods for exponential, power/logarithmic, and quadratic utility. When vanilla options are available for each underlying asset, the optimal solution is related to the fixed points of a Lipschitz map. In the case of exponential utility, there is only one such fixed point, and subsequent iterations of the map converge to it. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.00139&r=upt |
| By: | Cavve, Blake Stockton; Hurlstone, Mark J.; Farrell, Simon |
| Abstract: | Several distinct strategies or motivations have been proposed in order to characterise the ways in which people compare themselves to others, and how such information influences the decisions they make. Among the most studied type of social preference is inequality aversion, which describes a preference for equal outcomes for all group members, usually with a particular dislike for doing worse than others. A second, rank-status, describes the tendency to focus on the ordinal position (rather than the magnitude) of outcomes and the desire to rank higher than others in outcome standings. Though these competing forms of social preference describe very different psychological processes, these theories do—under certain circumstances—generate identical predictions. To accurately assess how people use information about others in decision-making, these theories must be deliberately, directly, and carefully disentangled. This paper presents two studies in which we competitively test these models of social preference as well as self-interest. We construct social utility curves from a series of satisfaction ratings of allocations for the self and one peer (Study 1) and two peer (Study 2) reference points. In both studies we find some heterogeneity expressed in preferences regarding distribution of several different attributes. Overall, a consistent plurality of participants are best fit by the Fehr and Schmidt inequality aversion model compared to mean reference fairness models and rank-based preference models; though a lesser proportion than found elsewhere in the literature (i.e., without comparison against competing models). Surprisingly, this preference is also prominent in considerations of vacation time, a leisure attribute assumed to be unaffected by social judgement. The results highlight both discrete and continuous individual differences in the form of social preference. |
| Date: | 2024–02–24 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:qkcm6&r=upt |
| By: | David Dillenberger (University of Pennsylvania); Uzi Segal (Boston College) |
| Abstract: | Consider an economy with equal amounts of N types of goods, to be allocated to agents with strict quasi-convex preferences over lotteries. We show that ex-ante, all feasible and Pareto efficient al- locations give almost all agents a binary lottery. Therefore, even if all preferences are the same, some identical agents necessarily receive different lotteries. Our results imply that many of the popular alloca- tion mechanisms used in practice are not ex-ante efficient. Assuming the reduction of compound lotteries axiom, social welfare deteriorates by first randomizing over these binary lotteries. Full ex-ante equality can be achieved if agents satisfy the compound independence axiom. |
| Keywords: | Allocation Problem, Binary Lotteries, Ex-Ante Efficiency, Matching, No-Envy, Non-Expected Utility, Quasi-Convex Preferences. |
| JEL: | C78 D61 D81 |
| Date: | 2024–03–03 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:1065&r=upt |
| By: | Burkhard C. Schipper |
| Abstract: | We consider a decision maker who is unaware of objects to be sampled and thus cannot form beliefs about the occurrence of particular objects. Ex ante she can form beliefs about the occurrence of novelty and the frequencies of yet to be known objects. Conditional on any sampled objects, she can also form beliefs about the next object being novel or being one of the previously sampled objects. We characterize behaviorally such beliefs under subjective expected utility. In doing so, we relate "reverse" Bayesianism, a central property in the literature on decision making under growing awareness, with exchangeable random partitions, the central property in the literature on the discovery of species problem and mutations in statistics, combinatorial probability theory, and population genetics. Partition exchangeable beliefs do not necessarily satisfy "reverse" Bayesianism. Yet, the most prominent models of exchangeable random partitions, the model by De Morgan (1838), the one parameter model of Ewens (1972), and the two parameter model of Pitman (1995) and Zabell (1997), do satisfy "reverse" Bayesianism. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.01421&r=upt |
| By: | Oumar Mbodji; Traian A. Pirvu |
| Abstract: | Merton portfolio management problem is studied in this paper within a stochastic volatility, non constant time discount rate, and power utility framework. This problem is time inconsistent and the way out of this predicament is to consider the subgame perfect strategies. The later are characterized through an extended Hamilton Jacobi Bellman (HJB) equation. A fixed point iteration is employed to solve the extended HJB equation. This is done in a two stage approach: in a first step the utility weighted discount rate is introduced and characterized as the fixed point of a certain operator; in the second step the value function is determined through a linear parabolic partial differential equation. Numerical experiments explore the effect of the time discount rate on the subgame perfect and precommitment strategies. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.05113&r=upt |
| By: | Sebastian Jaimungal; Xiaofei Shi |
| Abstract: | When an investor is faced with the option to purchase additional information regarding an asset price, how much should she pay? To address this question, we solve for the indifference price of information in a setting where a trader maximizes her expected utility of terminal wealth over a finite time horizon. If she does not purchase the information, then she solves a partial information stochastic control problem, while, if she does purchase the information, then she pays a cost and receives partial information about the asset's trajectory. We further demonstrate that when the investor can purchase the information at any stopping time prior to the end of the trading horizon, she chooses to do so at a deterministic time. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.11864&r=upt |
| By: | Felix Brandt; Matthias Greger; Erel Segal-Halevi; Warut Suksompong |
| Abstract: | We study the problem of aggregating distributions, such as budget proposals, into a collective distribution. An ideal aggregation mechanism would be Pareto efficient, strategyproof, and fair. Most previous work assumes that agents evaluate budgets according to the $\ell_1$ distance to their ideal budget. We investigate and compare different models from the larger class of star-shaped utility functions - a multi-dimensional generalization of single-peaked preferences. For the case of two alternatives, we extend existing results by proving that under very general assumptions, the uniform phantom mechanism is the only strategyproof mechanism that satisfies proportionality - a minimal notion of fairness introduced by Freeman et al. (2021). Moving to the case of more than two alternatives, we establish sweeping impossibilities for $\ell_1$ and $\ell_\infty$ disutilities: no mechanism satisfies efficiency, strategyproofness, and proportionality. We then propose a new kind of star-shaped utilities based on evaluating budgets by the ratios of shares between a given budget and an ideal budget. For these utilities, efficiency, strategyproofness, and fairness become compatible. In particular, we prove that the mechanism that maximizes the Nash product of individual utilities is characterized by group-strategyproofness and a core-based fairness condition. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.15904&r=upt |
| By: | Songyot Kitthamkesorn; Anthony Chen |
| Abstract: | Stochastic User Equilibrium (SUE) models depict the perception differences in traffic assignment problems. According to the assumption of an unbounded perceived travel time distribution, the conventional SUE problems result in a positive choice probability for all available routes, regardless of their unappealing travel time. This study provides an eUnit-SUE model to relax this assumption. The eUnit model is derived from a bounded probability distribution. This closed-form model aligns with an exponentiated random utility maximization (ERUM) paradigm with the exponentiated uniform distributed random error, where the lower and upper bounds endogeneously determine the route usage. Specifically, a Beckmann-type mathematical programming formulation is presented for the eUnit-SUE problem. The equivalency and uniqueness properties are rigorously proven. Numerical examples reveal that the eUnit bound range between the lower and upper bounds greatly affects the SUE assignment results. A larger bound range increases not only the number of routes in the choice set but also the degree of dispersion in the assignment results due to a larger route-specific perception variance. The misperception is contingent upon the disparity between the shortest and longest travel times and the bounds. As the bound range decreases, the shortest route receives significant flow allocation, and the assignment result approaches the deterministic user equilibrium (DUE) flow pattern. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.18435&r=upt |
| By: | Ata Atay; Christian Trudeau |
| Abstract: | Cooperative game theory aims to study how to divide a joint value created by a set of players. These games are often studied through the characteristic function form with transferable utility, which represents the value obtainable by each coalition. In the presence of externalities, there are many ways to define this value. Various models that account for different levels of player cooperation and the influence of external players on coalition value have been studied. Although there are different approaches, typically, the optimistic and pessimistic approaches provide sufficient insights into strategic interactions. This paper clarifies the interpretation of these approaches by providing a unified framework. We show that making sure that no coalition receives more than their (optimistic) upper bounds is always at least as difficult as guaranteeing their (pessimistic) lower bounds. We also show that if externalities are negative, providing these guarantees is always feasible. Then, we explore applications and show how our findings can be applied to derive results from the existing literature. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.01442&r=upt |
| By: | Natsuko Toba; Tooraj Jamasb; Luiz Maurer; Anupama Sen |
| Keywords: | Renewable energy, solar power, battery storage, auction design |
| JEL: | D0 D4 D8 L0 L1 L9 |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:enp:wpaper:eprg2312&r=upt |
| By: | Carina Cavalcanti (Department of Accounting, Finance and Economics, Griffith University, Southport and Nathan, QLD, Australia.); Andreas Leibbrandt (Department of Economics, Monash University, Clayton, VIC 3800, Australia.) |
| Abstract: | This field study investigates the characteristics and preferences of artisanal fishers who continue their profession in a lake afflicted by overfishing. We relate their economic preferences, fishing data, social networks, and socio-demographic information to their decision to either persist or discontinue fishing 4 and 15 years later. Our findings reveal that an increasing portion of fishers have chosen to cease fishing over time. We observe that the fisher’s risk preference is an important and robust factor for persistence: More risk-averse fishers are more likely to endure in their fishing endeavors. We also find evidence that better socially integrated, older and less educated individuals are more persistent. In contrast, we do not observe any notable relationships between persistence and the individual extent of overfishing or social preferences. These insights offer valuable novel knowledge regarding the evolving dynamics of resource user groups. By understanding these factors, policymakers and managers can optimize their approach to designing effective management practices and policies. |
| Keywords: | common pool resource, fishing, risk aversion |
| JEL: | C91 D81 H23 J24 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:mos:moswps:2024-04&r=upt |
| By: | Jozsef Konczer |
| Abstract: | This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are connected to Frequentist and Bayesian statistics, respectively. Later, a more general type of game is introduced, termed Statistical game, in which a further parameter, the players' relative risk aversion, can be set. In this work, we show that Fisher and Bayesian games can be viewed as limiting cases of Statistical games. Therefore, Statistical games can be viewed as a unified framework, incorporating both Frequentist and Bayesian statistics. Furthermore, a philosophical framework is (re-)presented -- often referred to as minimax regret criterion -- as a general approach to decision making. The main motivation for this work was to embed Bayesian statistics into a broader decision-making framework, where, based on collected data, actions with consequences have to be made, which can be translated to utilities (or rewards/losses) of the decision-maker. The work starts with the simplest possible toy model, related to hypothesis testing and statistical inference. This choice has two main benefits: i.) it allows us to determine (conjecture) the behaviour of the equilibrium strategies in various limiting cases ii.) this way, we can introduce Statistical games without requiring additional stochastic parameters. The work contains game theoretical methods related to two-player, non-cooperative games to determine and prove equilibrium strategies of Fisher, Bayesian and Statistical games. It also relies on analytical tools for derivations concerning various limiting cases. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2402.15892&r=upt |
| By: | Keisuke Kizaki (Mizuho-DL Financial Technology); Taiga Saito (School of Commerce, Senshu University); Akihiko Takahashi (Graduate School of Economics, The University of Tokyo) |
| Abstract: | This paper considers a multi-agent optimal investment problem with conservative, aggressive, or neutral sentiments in an incomplete market by a BSDE approach. Particularly, we formulate the conservative, aggressive, or neutral sentiments of the agents by a sup-inf/inf-sup, sup-sup, or sup problem where we take infimum or supremum on a choice of a probability measure depending on the view types and supremum on trading strategies. To the best of our knowledge, this is the first attempt to investigate a multi-agent equilibrium model in an incomplete setting with heterogeneous views on Brownian motions. Moreover, we show a square-root case where a group of agents has either conservative, aggressive, or neutral sentiments on the fundamental risks and a general case where the Sharpe ratio process of the risky asset and the optimal trading strategies in equilibrium are explicitly solved by a BSDE approach. Finally, we present numerical examples of the trading strategies and the expected return process in equilibrium under heterogeneous sentiments, which explain how the conservative, aggressive, or neutral sentiments affect the Sharpe ratio process of the risky asset and the trading strategies of the agents in equilibrium. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:cfi:fseres:cf578&r=upt |
| By: | Cary Deck (University of Alabama and Chapman University); Paan Jindapon (University of Alabama); Tigran Melkonyan (University of Alabama); Mark Schneider (University of Alabama) |
| Abstract: | Studies of ambiguity perceptions and attitudes are moving beyond the Ellsberg urn to examine people’s responses to ambiguity in naturally occurring events, games, and financial markets. In this study, we measure ambiguity perceptions and attitudes for market prices and allocations in four classical auction formats (first-price and second-price sealed bid auctions, English and Dutch clock auctions). We find ambiguity attitudes, representing individual preferences, are stable across auctions. However, the perceived ambiguity surrounding auction prices is lowest for English clock auctions which are obviously strategyproof (OSP), followed by second-price auctions which are strategyproof (SP), followed by a tie between first-price and Dutch clock auctions which are not strategyproof. Viewing OSP mechanisms as strategically simpler than SP mechanisms, and SP as strategically simpler than non-strategyproof mechanisms, our findings suggest ambiguity increases with strategic complexity. For allocations, we find perceived ambiguity is high for all four auction formats. |
| Keywords: | Ambiguity; Ambiguity Attitude; Auctions |
| JEL: | C9 D4 D8 |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:24-04&r=upt |
| By: | Angun, Ebru; Kleijnen, Jack (Tilburg University, Center For Economic Research) |
| Keywords: | risk aversion; chance constraint; inventory management; simulation optimization |
| Date: | 2024 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:a3a3e7ca-99a0-44bf-80c6-1541588d1997&r=upt |