
on Utility Models and Prospect Theory 
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 “certainuncertain” 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 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:117157&r=upt 
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 exante 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 inequityaverse behavior and stochastic shamemitigating behavior. Moreover, we discuss how our model can complement recent experimental evidence of expost and exante fairness concerns. 
Date:  2023–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2304.14977&r=upt 
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 gainloss 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 (piecewise) constant marginal utility which allows us to clearly separate the perception of uncertainty from the evaluation of outcomes. 
Date:  2023–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2304.14843&r=upt 
By:  AKIN, ZAFER; YAVAS, ABDULLAH 
Abstract:  We study whether and how the experimentally elicited risk and time preferences of subjects are associated with their behavior in longrun projects. First, risk and time preferences are elicited from timedated 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 (quasihyperbolic 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 longrun project. 
Keywords:  time preferences, quasihyperbolic discounting, experiment, longrun project 
JEL:  C91 D91 
Date:  2023–04–18 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:117133&r=upt 
By:  Sören Blomquist; Anil Kumar; CheYuan 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 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:31194&r=upt 
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 risktaking patterns obtained from certainty equivalents (CEs) to risktaking patterns observed when presenting all single choices contained in the CE lists onebyone 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 realworld decisions. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:rug:rugwps:23/1068&r=upt 
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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.04748&r=upt 
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 EuroMediterraneo per i Cambiamenti Climatici [Bologna]); Valentina Bosetti (Bocconi University [Milan, Italy], EIEE  European Institute on Economics and the Environment, CMCC  Centro EuroMediterraneo per i Cambiamenti Climatici [Bologna]) 
Abstract:  We report the results of two experiments designed to better understand the mechanisms driving decisionmaking 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 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal04071242&r=upt 
By:  Savchuk, Vladimir 
Abstract:  This presentation provides an overview of the various approaches and theories related to decisionmaking when faced with uncertainty. The paper's main focus is on the decisionmaking 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 decisionmaking 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 DecisionMaking process, achieved through the integration of the main components of the decisionmaking system under uncertainty, namely: (i) concepts of uncertainty, (ii) ways of thinking under uncertainty, (iii) creating models, and (iv) techniques of decisionmaking. 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 datadriven decisionmaking and nonquantitative 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 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:117213&r=upt 
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 shorterterm benefitcost 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 
URL:  http://d.repec.org/n?u=RePEc:rff:dpaper:dp2116&r=upt 
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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.01490&r=upt 
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 rankingsdependent utility implies that it may not be a dominant strategy to submit truthful preferences to a strategyproof mechanism, and that nonstrategyproof 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 nonstrategyproof 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 rankingsdependence 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 lowerranked goods. We find no differences between the two mechanisms for the rates of truthtelling and the final welfare. 
Date:  2023–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.03644&r=upt 
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 upto$\delta$ 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 welldefined. 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 NPhard to obtain a fully polynomial approximation scheme (FPTAS) for any constant robustness level. Nevertheless, we develop a quasipolynomial 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2304.14990&r=upt 
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 spendingutility 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.05134&r=upt 
By:  Loïc Berger (IÉSEG School Of Management [Puteaux], EIEE  European Institute on Economics and the Environment, CMCC  Centro EuroMediterraneo 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 decisionmaking 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 easytoimplement 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 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal04071230&r=upt 
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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2304.14631&r=upt 
By:  Paolo Galeazzi; Johannes Marti 
Abstract:  Following the decisiontheoretic 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2304.11575&r=upt 
By:  MohammadTaghi Hajiaghayi; Keivan Rezaei; Suho Shin 
Abstract:  We consider a multiagent delegated search without money, which is the first to study the multiagent 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 realworld scenarios, spanning classical economical applications to modern intelligent system. In stark contrast to singleagent setting by Kleinberg and Kleinberg (EC'18) with an approximate Bayesian mechanism, we show that there exist efficient approximate priorindependent 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 multiagent delegated search problem and derive several results on the approximation factors of Bayesian/priorindependent 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 multiagent setting ($n \ge 2$) over the singleagent 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 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2305.03203&r=upt 