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on Utility Models and Prospect Theory |
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Issue of 2022‒08‒15
eighteen papers chosen by |
| By: | Michael H. Freedman |
| Abstract: | The paper describes a funding mechanism called Quadratic Finance (QF) and deploys a bit of calculus to show that within a very clean and simple linear model QF maximizes social utility. They differentiate the social utility function. The mathematical content of this note is that by taking one further derivative, one may also deduce that QF is the unique solution. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.14711&r= |
| By: | Stéphan Sémirat (GAEL - Laboratoire d'Economie Appliquée de Grenoble - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes); Françoise Forges (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS - Centre National de la Recherche Scientifique - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres) |
| Abstract: | We consider a sender-receiver game, in which the sender has finitely many types and the receiver's decision is a real number. We assume that utility functions are concave, single-peaked and single-crossing. After the cheap talk phase, the receiver makes a decision, which requires the sender's approval to be implemented. Otherwise, the sender "exits". At a perfect Bayesian equilibrium without exit, the receiver must maximize his expected utility subject to the participation constraints of all positive probability types. This necessary condition may not hold at the receiver's prior belief, so that a non-revealing equilibrium may fail to exist. Similarly, a fully revealing equilibrium may not exist either due to the sender's incentive compatibility conditions.We propose a constructive algorithm that always achieves a perfect Bayesian equilibrium without exit. |
| Keywords: | Participation constraints,Discrete Cheap talk,Single-crossing |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03231673&r= |
| By: | Daske, Thomas; March, Christoph |
| Abstract: | This study explores mechanism design with allocation-based social preferences. Agents' social preferences and private payoffs are all subject to asymmetric information. We assume quasi-linear utility and independent types. We show how the asymmetry of information about agents' social preferences can be operationalized to satisfy agents' participation constraints. Our main result is a possibility result for groups of at least three agents: If endowments are sufficiently large, any such group can resolve any given allocation problem with an ex-post budget-balanced mechanism that is Bayesian incentive-compatible, interim individually rational, and ex-post Pareto-efficient. |
| Keywords: | mechanism design,social preferences,Bayesian implementation,participation constraints,participation stimulation |
| JEL: | C72 C78 D62 D82 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bamber:180&r= |
| By: | Brian Jabarian; Simon Lazarus |
| Abstract: | We conduct an incentivized experiment on a nationally representative US sample (N=708) to test how people prefer to avoid ambiguity even when the ambiguity improves the probability of receiving a fixed price. We find that subjects prefer non-ambiguous acts to similar ambiguous acts, even when the ambiguous acts provide larger win probabilities. Furthermore, this preference for avoiding ambiguity is not entirely due to a lack of understanding, as subjects "correctly" select the act with a larger win probability when comparing two similar ambiguous acts. Traditional models of ambiguity aversion cannot explain such preferences. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.04605&r= |
| By: | Salmerón Garrido, José Antonio; Nunno, Giulia Di; D'Auria, Bernardo |
| Abstract: | Default risk calculus emerges naturally in a portfolio optimization problem whenthe risky asset is threatened with a bankruptcy. The usual stochastic control techniques do not hold in this case and some additional assumptions are generally added to achieve the optimization in a before-and-after default context. We show how it is possible to avoid one of theses restrictive assumptions, the so-called Jacod density hypothesis, by using the framework of the forward integration. In particular, in the logarithmic utility case, in order to get the optimal portfolio the right condition it is proved to be the intensity hypothesis. We use the anticipating calculus to analyze the existence of the optimal portfolio for the logarithmic utility, and than under the assumption of existence of the optimal portfolio we prove the semimartingale decomposition of the risky asset in the filtration enlarged with the default process. |
| Keywords: | Optimal Portfolio; Default Risk; Progressive Enlargement; Forward Integrals; Malliavin Calculus |
| Date: | 2022–07–06 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:35411&r= |
| By: | Paolo Delle Site (UNICUSANO - University Niccolò Cusano); André de Palma (CY - CY Cergy Paris Université); Karim Kilani (LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - CNAM - Conservatoire National des Arts et Métiers [CNAM] - HESAM - HESAM Université - Communauté d'universités et établissements Hautes Ecoles Sorbonne Arts et Métiers Université) |
| Abstract: | We study the welfare change from project and policies when consumers' behaviour is described with additive random utility models. We consider the random compensating variation mainstream approach and review the latest methodological developments. The expectation of the random compensating variation is used as a measure of the average welfare change. Without income effect, it is expressed by the monetized difference of the expectations of the maximum utilities with and without the changes in monetary costs or quality. This measure reduces for the multinomial logit model to the logsum formula. More generally, the expectation of the compensating variation can be expressed as a path-independent line integral. The rule-of-a-half is an approximation of this line integral. With income effect, the expectation of the compensating variation, both unconditional and conditional on the choices without and with the changes, is provided by one-dimensional integrals which can be computed numerically. In the conditional case, the average welfare change is attributed to those keeping and those changing alternative. The cumulative distribution function of the compensating variation allows the analysis of inequalities by extending the classical Lorenz curve and Gini coefficient. This analysis is perfomed distinctly for positive and for negative values of the compensating variation. Treatment of observed and unobserved heterogeneity is included. The survey of theoretical results is illustrated with a numerical example in the context of transportation mode choice, based on large-scale data collected in France. |
| Keywords: | compensating variation,Gini coefficient,Lorenz curve,rule-of-a-half JEL codes: D11,D30,D60,R41,R42,R48,random utility model |
| Date: | 2022–07–10 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03719025&r= |
| By: | Michail Anthropelos; Paul Schneider |
| Abstract: | We consider portfolio selection under nonparametric $\alpha$-maxmin ambiguity in the neighbourhood of a reference distribution. We show strict concavity of the portfolio problem under ambiguity aversion. Implied demand functions are nondifferentiable, resemble observed bid-ask spreads, and are consistent with existing parametric limiting participation results under ambiguity. Ambiguity seekers exhibit a discontinuous demand function, implying an empty set of reservation prices. If agents have identical, or sufficiently similar prior beliefs, the first-best equilibrium is no trade. Simple conditions yield the existence of a Pareto-efficient second-best equilibrium, implying that heterogeneity in ambiguity preferences is sufficient for mutually beneficial transactions among all else homogeneous traders. These equilibria reconcile many observed phenomena in liquid high-information financial markets, such as liquidity dry-ups, portfolio inertia, and negative risk premia. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.10489&r= |
| By: | Leonard Hoeft (Humboldt University to Berlin); Michael Kurschilgen (Technical University of Munich, the Max Planck Institute for Research on Collective Goods, and the Stanford Graduate School of Business); Wladislaw Mill (University of Mannheim); Simone Vannuccini (Science Policy Research Unit, University of Sussex) |
| Abstract: | Economists model legal compliance as the process of maximizing utility while weighing the consequences from norm violation against other (monetary and non-monetary) considerations. Legal philosophers, on the other hand, believe that norms provide exclusionary reasons, i.e. that people apply the norm precisely to make a choice without weighing up on other issues. We test and compare both models in a controlled online experiment. We conduct a modified dictator game with partially unknown yet ascertainable payoffs, and vary between treatments the presence and content of authoritative norms. Our experimental results show that – in the presence of a norm – participants follow norms without searching for information that they deem important in the absence of a norm. This pattern is independent of the specific content of the norm. Our results are consistent with the legal model of norm compliance. |
| Keywords: | Norms, Information, Authority, Willful Ignorance, Dictator Game, Legal Theory, Experiment |
| JEL: | C91 D63 D81 D83 K10 |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:aiw:wpaper:22&r= |
| By: | Anton Kolotilin; Roberto Corrao; Alexander Wolitzky |
| Abstract: | In persuasion problems where the receiver's action is one-dimensional and his utility is single-peaked, optimal signals are characterized by duality, based on a first-order approach to the receiver's problem. A signal is optimal if and only if the induced joint distribution over states and actions is supported on a compact set (the contact set) where the dual constraint binds. A signal that pools at most two states in each realization is always optimal, and such pairwise signals are the only solutions under a non-singularity condition on utilities (the twist condition). We provide conditions under which higher actions are induced at more or less extreme pairs of states. Finally, we provide conditions for the optimality of either full disclosure or negative assortative disclosure, where signal realizations can be ordered from least to most extreme. Optimal negative assortative disclosure is characterized as the solution to a pair of ordinary differential equations. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.09164&r= |
| By: | Louis Kaplow |
| Abstract: | This article explores subjects in optimal income taxation characterized by recent research interest, practical importance in light of concerns about inequality, potential for misunderstanding, and prospects for advancement. Throughout, the analysis highlights paths for further investigation. Areas of focus include multidimensional abilities and endogenous wages; asymmetric information and the income of founders; production and consumption externalities from labor effort; market power and rents; behavioral phenomena relating to perceptions of the income tax schedule, myopic labor supply, and the interactions of savings, savings policies, and labor supply; optimal income transfers; the relationship between optimal income taxation and the use of other instruments; and issues relating to the social welfare function and utility functions, including nonwelfarist objectives, welfare weights, heterogeneous preferences, and taxation of the family. |
| JEL: | A13 D61 D62 D63 D82 D83 H20 H21 H23 H24 H41 H43 H53 H55 J22 L40 |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:30199&r= |
| By: | Alain Chateauneuf (IPAG Business School, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Bernard Cornet (KU - University of Kansas [Lawrence], CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | This paper studies arbitrage-free financial markets with bid-ask spreads whose super-hedging prices are submodular. The submodular assumption on the super-hedging price, or the supermodularity usually assumed on utility functions, is the formal expression of perfect complementarity, which dates back to Fisher, Pareto, and Edgeworth, according to Samuelson (J Econ Lit 12:1255–1289, 1974). Our main contribution provides several characterizations of financial markets with frictions that are submodular as a consequence of a more general study of submodular pricing rules. First, a market is submodular if and only if its super-hedging price is a Choquet integral and if and only if its set of risk-neutral probabilities is representable as the core of a submodular non-additive probability that is uniquely defined, called risk-neutral capacity. Second, a market is representable by its risk neutral capacity if and only if it is equivalent to a market, only composed of bid-ask event securities. |
| Keywords: | Submodularity,financial markets,Frictions,Bid-ask,Arbitrage,Multi-prior model,Super-hedging price,Super-replication,Risk measure,Pricing rules,Choquet integral,Event securities |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:hal-03722920&r= |
| By: | Marek Kapera |
| Abstract: | This paper provides theoretical foundations for preference discovery theory. We propose to relax the assumption that the consumer has perfect knowledge of their own preferences, so that the consumer knows only the subjective probability of those alternatives being in any given relation, which is conditional on the information available to the consumer. To achieve that, we construct probabilistic measures on the space of all permissible preference relations and consider the consumer to be equipped with one such measure, instead of a preference relation. These measures are intrinsically linked by construction to the information structure available to the consumer and allow for indirect learning. We visualize how these measures correspond to the choices of the consumer, we consider three distinct decision procedures. These procedures formalize how under different assumptions regarding the underlying probability measure, the consumer guesses their own tastes. Finally, we use these measures to define the value of the information provided by the consumption of a chosen alternative and study the properties of the preference ranking induced by it. |
| Keywords: | Taste uncertainty, Preference discovery, Learning through consumption, Conditional preferences, Experimental preferences |
| JEL: | D11 D83 D91 |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:sgh:kaewps:2022074&r= |
| By: | Tomasz R. Bielecki; Igor Cialenco; Andrzej Ruszczy\'nski |
| Abstract: | We consider a Markov decision process subject to model uncertainty in a Bayesian framework, where we assume that the state process is observed but its law is unknown to the observer. In addition, while the state process and the controls are observed at time $t$, the actual cost that may depend on the unknown parameter is not known at time $t$. The controller optimizes total cost by using a family of special risk measures, that we call risk filters and that are appropriately defined to take into account the model uncertainty of the controlled system. These key features lead to non-standard and non-trivial risk-averse control problems, for which we derive the Bellman principle of optimality. We illustrate the general theory on two practical examples: optimal investment and clinical trials. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.09235&r= |
| By: | Songjia Fan; Yi Tao; Cong Li |
| Abstract: | Selection shapes all kinds of behaviors, including how we make decisions under uncertainty. The risk attitude reflected from it should be simple, flexible, yet consistent. In this paper we engaged evolutionary dynamics to find the decision making rule concerning risk that is evolutionarily superior, and developed the theory of evolutionary rationality. We highlight the importance of selection intensity and fitness, as well as their equivalents in the human mind, named as attention degree and meta-fitness, in the decision making process. Evolutionary rationality targets the maximization of the geometric mean of meta-fitness (or fitness), and attention degree (or selection intensity) holds the key in the change of attitude of the same individual towards different events and under varied situations. Then as an example, the Allais paradox is presented to show the application of evolutionary rationality, in which the anomalous choices made by the majority of people can be well justified by a simple change in the attention degree. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.09813&r= |
| By: | Díaz, Antonia; Jerez, Belén; Rincón-Zapatero, Juan Pablo |
| Abstract: | This paper shows that, when utility is imperfectly transferable and the search process is competitive (or directed), wealthier buyers pay higher prices to speed up transactions. This result is established in a dynamic model of the housing market where households save both to smooth consumption and to build a down payment. "Block recursivity" is ensured by the existence of risk-neutral housing intermediaries. The calibrated version of our benchmark economy features greater indebtedness and higher housing prices in the long run compared to aWalrasian model, especially when the elasticity of new housing supply is low. We also show that the long-run effect of greater credit availability on housing prices depends crucially on whether or not rental and real estate housing stocks are segmented. Under full segmentation, price effects are much larger, with and without search frictions. But, even if there is no segmentation, these effects are substantial in our search model when supply elasticity is low, being larger than in the Walrasian version of the model. The last result is reversed with full segmentation, when search frictions dampen the price effect of the credit expansion. |
| Keywords: | Competitive Search; Wealth Effects; Housing Prices; Credit Constraints; Housing Supply Elasticity; Rental Market |
| JEL: | D31 D83 E21 R21 R30 |
| Date: | 2022–07–26 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:35536&r= |
| By: | Guanxing Fu |
| Abstract: | We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between the Nash equilibrium of the game and the solution to some FBSDE, which is proved to be equivalent to some BSDE. Our approach, which is general enough to cover power, exponential and log utilities, relies on martingale optimality principle in [3,9] and dynamic programming principle in [6,7]. When the market parameters do not depend on the Brownian paths, we get the unique Nash equilibrium in closed form. As a byproduct, when all market parameters are time-independent, we answer the question proposed in [12]: the strong equilibrium obtained in [12] is unique in the essentially bounded space. |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2206.05425&r= |
| By: | Peter J. Kuhn; Trevor T. Osaki |
| Abstract: | Using a vignette-based survey experiment on Amazon’s Mechanical Turk, we measure how people’s assessments of the fairness of race-based hiring decisions vary with the motivation and circumstances surrounding the discriminatory act and the races of the parties involved. Regardless of their political leaning, our subjects do not distinguish between taste-based and statistical discrimination, but they react in very similar ways to other aspects of the act, such as the quality of information on which statistical discrimination is based. Compared to conservatives, moderates and liberals are much less accepting of discriminatory actions, and consider the discriminatee’s race when making their fairness assessments. We describe four simple models of fairness –utilitarianism, race-blind rules (RBRs), racial in-group bias, and belief-based utilitarianism (BBU)-- and show that the latter two are inconsistent with major patterns in our data. Instead, we argue that a two-group model in which conservatives care only about race-blind rules (RBRs), while moderates and liberals care about both RBRs and utilitarian ethics can account for the main patterns we see. |
| JEL: | J71 |
| Date: | 2022–07 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:30236&r= |
| By: | Marie-Louise Leroux; Pierre Pestieau; Gregory Ponthiere |
| Abstract: | This paper studies the optimal design of assisted reproductive technologies (ART) policies in an economy where individuals differ in their reproductive capacity (or fecundity) and in their wage. We find that the optimal ART policy varies with the postulated social welfare criterion. Utilitarianism redistributes only between individuals with unequal fecundity and wages but not between parents and childless individuals. To the opposite, ex post egalitarianism (which gives absolute priority to the worst-off in realized terms) redistributes from individuals with children toward those without children, and from individuals with high fecundity toward those with low fecundity, so as to compensate for both the monetary cost of ART and for the disutility from involuntary childlessness resulting from unsuccessful ART investments. Under asymmetric information and in order to solve for the incentive problem, utilitarianism recommends also to either tax or subsidize ART investments of low-fecundity-low-productivity individuals depending on the degree of complementarity between fecundity and ART in the fertility technology. On the opposite, ex post egalitarianism always recommends marginal taxation. |
| Keywords: | fertility, assisted reproductive technologies, non-linear taxation, utilitarianism, ex-post egalitarianism |
| JEL: | H31 H51 I14 I18 J13 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9803&r= |