nep-upt New Economics Papers
on Utility Models and Prospect Theory
Issue of 2023‒05‒29
eighteen papers chosen by
Alexander Harin
Modern University for the Humanities

  1. To solve old problems of economics. The experimental background By Harin, Alexander
  2. Social Preferences and Deliberately Stochastic Behavior By Yosuke Hashidate; Keisuke Yoshihara
  3. Gain-Loss Hedging and Cumulative Prospect Theory By Lorenzo Bastianello; Alain Chateauneuf; Bernard Cornet
  4. Elicited Time Preferences and Behavior in Long-Run Projects By AKIN, ZAFER; YAVAS, ABDULLAH
  5. Nonlinear Budget Set Regressions for the Random Utility Model By Sören Blomquist; Anil Kumar; Che-Yuan Liang; Whitney Newey
  6. Choice lists and ‘standard patterns’ of risk-taking By Ranoua Bouchouicha; Jilong Wu; Ferdinand M. Vieider
  7. A greedy algorithm for habit formation under multiplicative utility By Snezhana Kirusheva; Thomas S. Salisbury
  8. Unraveling Ambiguity Aversion By Ilke Aydogan; Loïc Berger; Valentina Bosetti
  9. Making Decisions under Uncertainty: Value Chain Development By Savchuk, Vladimir
  10. A Discounting Rule for the Social Cost of Carbon By Newell, Richard G.; Pizer, William; Prest, Brian C.
  11. Optimal control problems for stochastic processes with absorbing regime By yaacov Kopeliovich
  12. Rankings-Dependent Preferences: A Real Goods Matching Experiment By Andrew Kloosterman; Peter Troyan
  13. Robust Stackelberg Equilibria By Jiarui Gan; Minbiao Han; Jibang Wu; Haifeng Xu
  14. To AI or not to AI, to Buy Local or not to Buy Local: A Mathematical Theory of Real Price By Huan Cai; Catherine Xu; Weiyu Xu
  15. A Randomness Device to Create the Conidtions of Uncertainty By Loïc Berger
  16. Nontransitive Preferences and Stochastic Rationalizability: A Behavioral Equivalence By Mogens Fosgerau; John Rehbeck
  17. Choice Structures in Games By Paolo Galeazzi; Johannes Marti
  18. Multi-agent Delegated Search By MohammadTaghi Hajiaghayi; Keivan Rezaei; Suho Shin

  1. By: Harin, Alexander
    Abstract: Old problems of the mathematical description of the economical behavior of a man are briefly reviewed. They are a comparison of choices of a man between uncertain and sure games and the radically different behavior of a man in different domains. The proposed solution of the problems consists in purely mathematical method and models and is briefly reviewed in the Appendix. The main attention is paid to the analysis of the experimental support of this possible solution. The generally accepted random incentive experimental procedures are discussed. A “certain-uncertain” inconsistency between the certain type of the choices and the uncertain type of the incentives is revealed and analyzed.
    Keywords: behavior; decision; prospect theory; utility; experiment; incentive; economics;
    JEL: C1 C9 C91 C93 D8 D81
    Date: 2023–04–26
  2. By: Yosuke Hashidate; Keisuke Yoshihara
    Abstract: This study proposes a tractable stochastic choice model to identify motivations for prosocial behavior, and to explore alternative motivations of deliberate randomization beyond ex-ante fairness concerns. To represent social preferences, we employ an additively perturbed utility model consisting of the sum of expected utility and a nonlinear cost function, where the utility function is purely selfish while the cost function depends on social preferences. Using the cost function, we study stochastic choice patterns to distinguish between stochastic inequity-averse behavior and stochastic shame-mitigating behavior. Moreover, we discuss how our model can complement recent experimental evidence of ex-post and ex-ante fairness concerns.
    Date: 2023–04
  3. By: Lorenzo Bastianello; Alain Chateauneuf; Bernard Cornet
    Abstract: Two acts are comonotonic if they yield high payoffs in the same states of nature. 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 simpler case of (piece-wise) constant marginal utility which allows us to clearly separate the perception of uncertainty from the evaluation of outcomes.
    Date: 2023–04
    Abstract: We study whether and how the experimentally elicited risk and time preferences of subjects are associated with their behavior in long-run projects. First, risk and time preferences are elicited from time-dated monetary choices to estimate a general discount and utility function at an individual level, then subjects work on a longitudinal project that requires effort in multiple periods. We find that present bias in the form of a fixed cost or variable cost (quasi-hyperbolic discounting) is not supported by monetary choices. Analyses of allocation patterns of work reveal that the estimated utility and discounting models are not compatible with the observed allocations. We find evidence of both present and future bias, although the former is more prevalent and severe, and subjects exhibit naivete in their choice reversals. Furthermore, discount rate and present bias parameters estimated based on monetary choices have predictive power on how work is allocated in the long-run project.
    Keywords: time preferences, quasi-hyperbolic discounting, experiment, long-run project
    JEL: C91 D91
    Date: 2023–04–18
  5. By: Sören Blomquist; Anil Kumar; Che-Yuan Liang; Whitney Newey
    Abstract: This paper is about the nonparametric regression of a choice variable on a nonlinear budget set under utility maximization with general heterogeneity, i.e. in the random utility model (RUM). We show that utility maximization and convex budget sets make this regression three dimensional with a more parsimonious specification than previously derived. We show that nonconvexities in the budget set will have little effect on these results in important cases. We characterize all the restrictions of utility maximization on the budget set regression and show how to check these restrictions in applications. We formulate budget set effects that can be identified by this regression and give automatic debiased machine learners of these effects. We consider use of control functions to allow for endogeneity. Throughout we take as the main example the effect of taxes on taxable income including accounting for productivity growth. In an application to Swedish data we find the taxable income elasticity of a change in the slope of each segment to be .52, that the regression satisfies the restrictions of utility maximization at the values chosen for over 95% of observations, and that a productivity growth rate we estimate is close to other estimates.
    JEL: C14 C24 H31 J22
    Date: 2023–04
  6. By: Ranoua Bouchouicha; Jilong Wu; Ferdinand M. Vieider (-)
    Abstract: The fourfold pattern of risk attitudes has been called ‘the most distinctive implication of prospect theory’. It constitutes the central mechanism by which prospect theory (PT) explains the coexistence of gambling and insurance. Here, we compare risk-taking patterns obtained from certainty equivalents (CEs) to risk-taking patterns observed when presenting all single choices contained in the CE lists one-by-one in a binary choice setup. Choices obtained from CEs indicate a clear fourfold pattern. Binary choices, on the other hand, indicate risk aversion for small probability gains, and risk seeking for small probabilities losses—the opposite of what is predicted by the fourfold pattern. The use of CEs to measure PT parameters is often justified based on the fact that they avoid endogenous reference points, which have been documented by comparing CEs to probability equivalents (PEs). We show that loss aversion in a PT model can actually not account for this discrepancy, since the gap between CEs and PEs requires different loss aversion coefficients for each PE task. Our results thus question the applicability of PT beyond the restrictive realm of CEs, which are arguably a poor proxy for most real-world decisions.
    Date: 2023–05
  7. By: Snezhana Kirusheva; Thomas S. Salisbury
    Abstract: We consider the problem of optimizing lifetime consumption under a habit formation model, both with and without an exogenous pension. Unlike much of the existing literature, we apply a power utility to the ratio of consumption to habit, rather than to their difference. The martingale/duality method becomes intractable in this setting, so we develop a greedy version of this method that is solvable using Monte Carlo simulation. We investigate the behaviour of the greedy solution, and explore what parameter values make the greedy solution a good approximation to the optimal one.
    Date: 2023–05
  8. By: Ilke Aydogan (IÉSEG School Of Management [Puteaux]); Loïc Berger (CNRS - Centre National de la Recherche Scientifique, IÉSEG School Of Management [Puteaux], EIEE - European Institute on Economics and the Environment, CMCC - Centro Euro-Mediterraneo per i Cambiamenti Climatici [Bologna]); Valentina Bosetti (Bocconi University [Milan, Italy], EIEE - European Institute on Economics and the Environment, CMCC - Centro Euro-Mediterraneo per i Cambiamenti Climatici [Bologna])
    Abstract: We report the results of two experiments designed to better understand the mechanisms driving decision-making under ambiguity. We elicit individual preferences over different sources of uncertainty (risk, compound risk, model ambiguity, and Ellsberg ambiguity), which entail different degrees of complexity, from subjects with different sophistication levels. We show that (1) ambiguity aversion is robust to sophistication, but the strong relationship that has been previously reported between attitudes toward ambiguity and compound risk is not. (2) Ellsberg ambiguity attitude can be partly explained by attitudes toward complexity for less sophisticated subjects, but not for more sophisticated ones. Overall, and regardless of the subject's sophistication level, the main driver of Ellsberg ambiguity attitude is a specific treatment of unknown probabilities. These results leave room for using ambiguity models in applications with prescriptive purposes.
    Keywords: Ambiguity aversion, complexity, reduction of compound risk, model uncertainty
    Date: 2023–04–17
  9. By: Savchuk, Vladimir
    Abstract: This presentation provides an overview of the various approaches and theories related to decision-making when faced with uncertainty. The paper's main focus is on the decision-making process itself, including how all its various components should be combined and how they should be reflected in decision rules. While the theme is not new, significant progress has been made in the past century in terms of developing decision-making techniques and measuring and managing uncertainty, largely due to the advancements in probability theory and fuzzy set theory. The goal of this paper is to develop a Value Chain for the Decision-Making process, achieved through the integration of the main components of the decision-making system under uncertainty, namely: (i) concepts of uncertainty, (ii) ways of thinking under uncertainty, (iii) creating models, and (iv) techniques of decision-making. These issues are considered in their dialectical relationship. The presentation will not delve into the specifics of each part of the system but rather aims to explain its essence and practical applicability. Both data-driven decision-making and non-quantitative approaches to making decisions are explored in the presentation.
    Keywords: Uncertainty, Risk, Probability, Fuzzy sets, Metaphor, Narrative, Decision Theory, Expected Utility Theory, Prospect Theory, Possibility Theory, Real Options.
    JEL: M21
    Date: 2022–11
  10. By: Newell, Richard G. (Resources for the Future); Pizer, William (Resources for the Future); Prest, Brian C. (Resources for the Future)
    Abstract: We develop a discounting rule for estimating the social cost of carbon (SCC) given uncertain economic growth. Diminishing marginal utility of income implies a relationship between the discount rate term structure and economic growth uncertainty. In the classic Ramsey framework, this relationship is governed by parameters reflecting pure time preference and the elasticity of the marginal utility of consumption; yet disagreement remains about the values of these parameters. We calibrate these parameters to match empirical evidence on both the future interest rate term structure and economic growth uncertainty, while also maintaining consistency with discount rates used for shorter-term benefit-cost analysis. Such an integrated approach is crucial amidst growth uncertainty, where growth is also a key determinant of climate damages. This results in an empirically driven, stochastic discounting rule to be used in estimating the SCC that also accounts for the correlation between climate damage estimates and discount rates.
    Date: 2021–06–18
  11. By: yaacov Kopeliovich
    Abstract: In this paper we formulate and solve an optimal problem for Stochastic process with a regime absorbing state. The solution for this problem is obtained through a system of partial differential equations. The method is applied to obtain an explicit solution for the Merton portfolio problem when an asset has a default probability in case of a log utility.
    Date: 2023–05
  12. By: Andrew Kloosterman; Peter Troyan
    Abstract: We investigate whether preferences for objects received via a matching mechanism are influenced by how highly agents rank them in their reported rank order list. We hypothesize that all else equal, agents receive greater utility for the same object when they rank it higher. The addition of rankings-dependent utility implies that it may not be a dominant strategy to submit truthful preferences to a strategyproof mechanism, and that non-strategyproof mechanisms that give more agents objects they report as higher ranked may increase market welfare. We test these hypotheses with a matching experiment in a strategyproof mechanism, the random serial dictatorship, and a non-strategyproof mechanism, the Boston mechanism. A novel feature of our experimental design is that the objects allocated in the matching markets are real goods, which allows us to directly measure rankings-dependence by eliciting values for goods both inside and outside of the mechanism. Our experimental results confirm that the elicited differences in values do decrease for lower-ranked goods. We find no differences between the two mechanisms for the rates of truth-telling and the final welfare.
    Date: 2023–05
  13. By: Jiarui Gan; Minbiao Han; Jibang Wu; Haifeng Xu
    Abstract: This paper provides a systematic study of the robust Stackelberg equilibrium (RSE), which naturally generalizes the widely adopted solution concept of the strong Stackelberg equilibrium (SSE). The RSE accounts for any possible up-to-$\delta$ suboptimal follower responses in Stackelberg games and is adopted to improve the robustness of the leader's strategy. While a few variants of robust Stackelberg equilibrium have been considered in previous literature, the RSE solution concept we consider is importantly different -- in some sense, it relaxes previously studied robust Stackelberg strategies and is applicable to much broader sources of uncertainties. We provide a thorough investigation of several fundamental properties of RSE, including its utility guarantees, algorithmics, and learnability. We first show that the RSE we defined always exists and thus is well-defined. Then we characterize how the leader's utility in RSE changes with the robustness level considered. On the algorithmic side, we show that, in sharp contrast to the tractability of computing an SSE, it is NP-hard to obtain a fully polynomial approximation scheme (FPTAS) for any constant robustness level. Nevertheless, we develop a quasi-polynomial approximation scheme (QPTAS) for RSE. Finally, we examine the learnability of the RSE in a natural learning scenario, where both players' utilities are not known in advance, and provide almost tight sample complexity results on learning the RSE. As a corollary of this result, we also obtain an algorithm for learning SSE, which strictly improves a key result of Bai et al. in terms of both utility guarantee and computational efficiency.
    Date: 2023–04
  14. By: Huan Cai; Catherine Xu; Weiyu Xu
    Abstract: In the past several decades, the world's economy has become increasingly globalized. On the other hand, there are also ideas advocating the practice of ``buy local'', by which people buy locally produced goods and services rather than those produced farther away. In this paper, we establish a mathematical theory of real price that determines the optimal global versus local spending of an agent which achieves the agent's optimal tradeoff between spending and obtained utility. Our theory of real price depends on the asymptotic analysis of a Markov chain transition probability matrix related to the network of producers and consumers. We show that the real price of a product or service can be determined from the involved Markov chain matrix, and can be dramatically different from the product's label price. In particular, we show that the label prices of products and services are often not ``real'' or directly ``useful'': given two products offering the same myopic utility, the one with lower label price may not necessarily offer better asymptotic utility. This theory shows that the globality or locality of the products and services does have different impacts on the spending-utility tradeoff of a customer. The established mathematical theory of real price can be used to determine whether to adopt or not to adopt certain artificial intelligence (AI) technologies from an economic perspective.
    Date: 2023–05
  15. By: Loïc Berger (IÉSEG School Of Management [Puteaux], EIEE - European Institute on Economics and the Environment, CMCC - Centro Euro-Mediterraneo per i Cambiamenti Climatici [Bologna], LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique)
    Abstract: The experimental study of decision-making under uncertainty typically builds on Ellsberg's (1961) setting. Yet, as the total number of balls is known in standard Ellsberg's urns, an implicit constraint is put on the specification of the probability models to consider. In practice, this restricts the ability of Ellsberg's urns to characterize situations going beyond those of model ambiguity. In this note, I present a simple and easy-to-implement device that creates the initial conditions of uncertainty, which constitute a critical prerequisite for the study of model misspecification.
    Keywords: Ambiguity aversion, experiment, Ellsberg paradox, model uncertainty
    Date: 2023–04–17
  16. By: Mogens Fosgerau; John Rehbeck
    Abstract: Nontransitive choices have long been an area of curiosity within economics. However, determining whether nontransitive choices represent an individual's preference is a difficult task since choice data is inherently stochastic. This paper shows that behavior from nontransitive preferences under a monotonicity assumption is equivalent to a transitive stochastic choice model. In particular, nontransitive preferences are regularly interpreted as a strength of preference, so we assume alternatives are chosen proportionally to the nontransitive preference. One implication of this result is that one cannot distinguish ``complementarity in attention" and ``complementarity in demand."
    Date: 2023–04
  17. By: Paolo Galeazzi; Johannes Marti
    Abstract: Following the decision-theoretic approach to game theory, we extend the analysis of Epstein & Wang and of Di Tillio from hierarchies of preference relations to hierarchies of choice functions. We then construct the universal choice structure containing all these choice hierarchies, and show how the universal preference structure of Di Tillio is embedded in it.
    Date: 2023–04
  18. By: MohammadTaghi Hajiaghayi; Keivan Rezaei; Suho Shin
    Abstract: We consider a multi-agent delegated search without money, which is the first to study the multi-agent extension of Kleinberg and Kleinberg (EC'18). In our model, given a set of agents, each agent samples a fixed number of solutions, and privately sends a signal, e.g., a subset of solutions, to the principal. Then, the principal selects a final solution based on the agents' signals. Our model captures a variety of real-world scenarios, spanning classical economical applications to modern intelligent system. In stark contrast to single-agent setting by Kleinberg and Kleinberg (EC'18) with an approximate Bayesian mechanism, we show that there exist efficient approximate prior-independent mechanisms with both information and performance gain, thanks to the competitive tension between the agents. Interestingly, however, the amount of such a compelling power significantly varies with respect to the information available to the agents, and the degree of correlation between the principal's and the agent's utility. Technically, we conduct a comprehensive study on the multi-agent delegated search problem and derive several results on the approximation factors of Bayesian/prior-independent mechanisms in complete/incomplete information settings. As a special case of independent interest, we obtain comparative statics regarding the number of agents which implies the dominance of the multi-agent setting ($n \ge 2$) over the single-agent setting ($n=1$) in terms of the principal's utility. We further extend our problem by considering an examination cost of the mechanism and derive some analogous results in the complete information setting.
    Date: 2023–05

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