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on Utility Models and Prospect Theory |
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Issue of 2019‒02‒04
twenty-two papers chosen by |
| By: | Beißner, Patrick (Center for Mathematical Economics, Bielefeld University); Lin, Qian (Center for Mathematical Economics, Bielefeld University); Riedel, Frank (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | The α-maxmin model is a prominent example of preferences under Knightian uncertainty as it allows to distinguish ambiguity and ambiguity attitude. These preferences are dynamically inconsistent for nontrivial versions of α. In this paper, we derive a recursive, dynamically consistent version of the α-maxmin model. In the continuous-time limit, the resulting dynamic utility function can be represented as a convex mixture between worst and best case, but now at the local, infinitesimal level. We study the properties of the utility function and provide an Arrow- Pratt approximation of the static and dynamic certainty equivalent. We derive a consumption-based capital asset pricing formula and study the implications for derivative valuation under indifference pricing. |
| Keywords: | Dynamic consistency, α-maxmin expected utility, Knightian uncertainty, ambiguity attitude |
| Date: | 2018–08–16 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:593&r=all |
| By: | Martina Nardon (Department of Economics, Cà Foscari University Of Venice); Paolo Pianca (Department of Economics, Cà Foscari University Of Venice) |
| Abstract: | We define a premium principle under the continuous cumulative prospect theory which extends the equivalent utility principle. In prospect theory risk attitude and loss aversion are shaped via a value function, whereas a transformation of objective probabilities, which is commonly referred as probability weighting, models probabilistic risk perception. In cumulative prospect theory, probabilities of individual outcomes are replaced by decision weights, which are differences in transformed, through the weighting function, counter-cumulative probabilities of gains and cumulative probabilities of losses, with outcomes ordered from worst to best. Empirical evidence suggests a typical inverse-S shaped function: decision makers tend to overweight small probabilities, and underweight medium and high probabilities; moreover, the probability weighting function is initially concave and then convex. We study some properties of the behavioral premium principle. We also assume an alternative framing of the outcomes; then we discuss several applications to the pricing of insurance contracts. |
| Keywords: | Continuous Cumulative Prospect Theory, Insurance Premium Principles, Zero Utility Principle, Framing, Probability Weighting Function |
| JEL: | D81 G22 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2019:03&r=all |
| By: | Misha Perepelitsa |
| Abstract: | We consider a model for decision making based on an adaptive, k-period, learning process where the priors are selected according to Von Neumann-Morgenstern expected utility principle. A preference relation between two prospects is introduced, defined by the condition which prospect is selected more often. We show that the new preferences have similarities with the preferences obtained by Kahneman and Tversky (1979) in the context of the prospect theory. Additionally, we establish that in the limit of large learning period, the new preferences coincide with the expected utility principle. |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1901.04995&r=all |
| By: | Fabian Herweg; Daniel Müller |
| Abstract: | Two non-expected-utility-theory approaches to model decision making under risk are regret theory (Loomes and Sugden, 1982; Bell, 1982) and salience theory (Bordalo, Gennaioli, and Shleifer, 2012). While the psychological underpinning of these two approaches is different, the models share the assumption that within-state comparisons of outcomes across choice options are a key determinant of choice behavior. We investigate the overlap between the two theories and show that salience theory is a special case of regret theory. Moreover, we trace out the relationship be- tween diminishing sensitivity of the salience function and concavity of the choiceless utility function with regard to behavioral implications. |
| Keywords: | choice under risk, regret theory, salience theory |
| JEL: | D81 D91 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7445&r=all |
| By: | Tanner, Noam (Federal Reserve Bank of Boston) |
| Abstract: | A principal is uncertain of an agent's preferences and cannot provide monetary transfers. The principal, however, does control the discretion granted to the agent. In this paper, we provide a simple characterization of when it is optimal for the principal to screen by offering different terms of discretion to the agent. When the principal's utility is sufficiently concave, it is optimal for the principal to pool and to offer all agents the same discretion. Thus, for any number of agents and any distribution over agent preferences, the optimal contract is simple: the principal sets a cap and forbids actions above this cap (interval delegation). For less concave preferences, it is optimal for the principal to screen. The principal benefits by providing agents a choice between interval delegation and gap delegation, which allows for more extreme actions but prohibits intermediate actions. Moreover, we provide new intuition for the optimality of interval delegation when the principal knows the agent's preferences: the payoff distributions generated by sets containing gaps are mean-preserving spreads of those generated by intervals. |
| Keywords: | Optimal delegation; Sequential screening; Dynamic mechanism design; Non-transferable utility |
| JEL: | D02 D20 D82 D86 |
| Date: | 2018–03–30 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedbqu:rpa18-1&r=all |
| By: | Sandro Sozzo |
| Abstract: | {\it Ellsberg thought experiments} and empirical confirmation of Ellsberg preferences pose serious challenges to {\it subjective expected utility theory} (SEUT). We have recently elaborated a quantum-theoretic framework for human decisions under uncertainty which satisfactorily copes with the Ellsberg paradox and other puzzles of SEUT. We apply here the quantum-theoretic framework to the {\it Ellsberg two-urn example}, showing that the paradox can be explained by assuming a state change of the conceptual entity that is the object of the decision ({\it decision-making}, or {\it DM}, {\it entity}) and representing subjective probabilities by quantum probabilities. We also model the empirical data we collected in a DM test on human participants within the theoretic framework above. The obtained results are relevant, as they provide a line to model real life, e.g., financial and medical, decisions that show the same empirical patterns as the two-urn experiment. |
| Date: | 2018–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1811.00875&r=all |
| By: | von Wangenheim, Jonas |
| Abstract: | Evidence suggests that people evaluate outcomes relative to expectations. I analyze this expectation-based loss aversion (Köszegi and Rabin (2006, 2009)) in the context of dynamic and static auctions, where the reference point is given by the (endogenous) equilibrium outcome. If agents update their reference point during the auction, the arrival of information crucially affects equilibrium behavior. Consequently, I show that - even with independent private values - the Vickrey auction yields strictly higher revenue than the English auction, violating the well known revenue equivalence. Thus, dynamic loss aversion offers a novel explanation for empirically observed differences between these auction formats. |
| Keywords: | Vickrey auction,English auction,expectation-based loss aversion,revenue equivalence,dynamic loss aversion,personal equilibrium |
| JEL: | D03 D44 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:fubsbe:20191&r=all |
| By: | Gabriel Ziegler; Peio Zuazo-Garin |
| Abstract: | Economic predictions often hinge on two intuitive premises: agents rule out the possibility of others choosing unreasonable strategies (‘strategic reasoning’), and prefer strategies that hedge against unexpected behavior (‘cautiousness’). These two premises conflict and this undermines the compatibility of usual economic predictions with reasoning-based foundations. This paper proposes a new take on this classical tension by interpreting cautiousness as robustness to ambiguity. We formalize this via a model of incomplete preferences, where (i) each player’s strategic uncertainty is represented by a possibly non-singleton set of beliefs and (ii) a rational player chooses a strategy that is a best-reply to every belief in this set. We show that the interplay between these two features precludes the conflict between strategic reasoning and cautiousness and therefore solves the inclusion-exclusion problem raised by Samuelson (1992). Notably, our approach provides a simple foundation for the iterated elimination of weakly dominated strategies |
| Keywords: | Game theory, decision theory, ambiguity, Knightian uncertainty, incomplete preferences, Bayesian rationality, cautiousness, iterated admissibility |
| JEL: | C72 D82 |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1630&r=all |
| By: | Murwirapachena, Genius; Dikgang, Johane |
| Abstract: | Choice experiments typically include a status quo option, which often describes the current scenario. This is to secure the validity and applicability of choice experiments. People have a propensity to choose what they are familiar with, despite being presented with alternatives that seem better (i.e. the ‘status quo effect’). Various experiments have reliably demonstrated this effect. The tendency to prefer the current scenario disproportionally does not mimic real-life preferences; therefore, status quo bias is undesirable. In a split sample framework, we test for the effects of reducing status quo bias by considering a heterogeneous sample. We use generalised mixed logit models to carry out the tests. The tests reveal that presenting each split sample with a partially relevant status quo significantly reduces the status quo bias problem. |
| Keywords: | choice experiments, heterogeneous, generalised mixed logit, status quo bias. |
| JEL: | H41 Q25 Q51 |
| Date: | 2018–12–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:91549&r=all |
| By: | Daniel Kraehmer; |
| Abstract: | I study mechanism design settings with quasi-linear utility where the principal can provide agents with additional private information about their valuations beyond the private information they hold at the outset. I demonstrate that the principal can design information and a mechanism so as to fully extract the complete information first-best surplus if agents’ ex ante information only affects their beliefs about, yet not their valuations. Otherwise, the result holds if each agent’s initial private beliefs satisfy a spanning condition. |
| Keywords: | information design, mechanism design, quasi-linear utility, rent extraction |
| JEL: | D82 H57 |
| Date: | 2018–04 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2018_011&r=all |
| By: | Thomas Dohmen; Simone Quercia; Jana Willrodt |
| Abstract: | We show that the disposition to focus on favorable or unfavorable outcomes of risky situations affects willingness to take risk as measured by the general risk question. We demonstrate that this disposition, which we call risk conception, is strongly associated with optimism, a stable facet of personality and that it predicts real-life risk taking. The general risk question captures this disposition alongside pure risk preference. This enlightens why the general risk question is a better predictor of behavior under risk across different domains than measures of pure risk preference. Our results also rationalize why risk taking is related to optimism. |
| Keywords: | risk taking behavior, optimism, preference measures, risk conception |
| JEL: | D91 C91 D81 D01 |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2018_023&r=all |
| By: | Giuseppe De Marco (Università di Napoli Parthenope and CSEF) |
| Abstract: | The Shafer and Sonnenshein convexity of preferences is a key property in game theory. Previous research has shown that, in case of decisions under uncertainty, the compliance with this property (jointly) depends on the concavity/convexity of the imprecise probabi- listic model with respect to the decision variable and on the attitudes towards imprecision of the decision maker. The present paper deepens the analysis by looking at set-valued imprecise probabilistic models that encompass sets of probability distributions and sets of almost desirable gambles. Moreover, it is shown that the required Shafer and Sonnenshein convexity property is obtained also in case the imprecise probability correspondences satisfy quasi-concavity/convexity with respect to the decision variable so that the set of admissible probabilistic models is significantly broadened. It is well known that sets of probability distributions and sets of almost desirable gambles are general models of representation of uncertainty that are connected to each other; moreover, they are both related to another model known as lower expectation. Therefore, the second part of this work explores the links between the (quasi-)concavity/convexity properties accross the three different models so as to understand to what extent the Shafer and Sonnenshein convexity results hold. |
| Keywords: | Convex preferences, Imprecise probabilities, quasi-concavity/convexity, set-valued maps |
| Date: | 2019–01–15 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:523&r=all |
| By: | Han Qiu |
| Abstract: | In this study, we consider traveler coupon redemption behavior from the perspective of an urban mobility service. Assuming traveler behavior is in accordance with the principle of utility maximization, we first formulate a baseline dynamical model for traveler's expected future trip sequence under the framework of Markov decision processes and from which we derive approximations of the optimal coupon redemption policy. However, we find that this baseline model cannot explain perfectly observed coupon redemption behavior of traveler for a car-sharing service. To resolve this deviation from utility-maximizing behavior, we suggest a hypothesis that travelers may not be aware of all coupons available to them. Based on this hypothesis, we formulate an inattention model on unawareness, which is complementary to the existing models of inattention, and incorporate it into the baseline model. Estimation results show that the proposed model better explains the coupon redemption dataset than the baseline model. We also conduct a simulation experiment to quantify the negative impact of unawareness on coupons' promotional effects. These results can be used by mobility service operators to design effective coupon distribution schemes in practice. |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1901.05070&r=all |
| By: | Rava Azeredo da Silveira; Michael Woodford |
| Abstract: | We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannon’s mutual information, as in models of rational inattention; but our theory differs from that of Sims (2003) in not assuming costless memory of past cognitive states. We show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rational-expectations (perfect-memory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of expectations in laboratory and field settings, most notably apparent over-reaction of both elicited forecasts and spending decisions to transitory fluctuations in economic time series. |
| JEL: | D91 |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:25478&r=all |
| By: | de Blasio, Guido (Bank of Italy); De Paola, Maria (University of Calabria); Poy, Samuele (Università Cattolica del Sacro Cuore); Scoppa, Vincenzo (University of Calabria) |
| Abstract: | This paper investigates the impact of risk attitudes on the decision to become an entrepreneur. In contrast to previous research, we handle endogeneity issues relying on an instrumental variables strategy considering as a source of exogenous variation in risk aversion the early exposure to a massive earthquake. Using several waves of the Bank of Italy Survey of Household Income and Wealth (SHIW), we find that individuals experiencing an earthquake become significantly more risk averse. Second-stage estimates show that risk aversion has a significant negative impact on the probability of becoming an entrepreneur. |
| Keywords: | entrepreneurship, risk attitudes, natural disasters, instrumental variables |
| JEL: | D81 D91 L26 C36 |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp12057&r=all |
| By: | James Banks (Institute for Fiscal Studies and University of Manchester); Elena Bassoli (Department of Economics, University Of Venice Cà Foscari); Irene Mammi (Department of Economics, University Of Venice Cà Foscari) |
| Abstract: | This paper investigates risk preference at older ages in 14 European countries. Older individuals report greater risk aversion. Using the longitudinal nature of the data we are able to show this relationship between risk preferences and age is not due to cohort effects or selective mortality. We also show, however, that on average roughly forty percent of this overall age effect is actually due to life events such as retirement, health shocks and widowhood or marital change that occur increasingly as individuals age. These life events are a particularly important explanation of the age `effect' for women and for the age group 50-64. |
| Keywords: | Risk attitude, ageing, health status, life-related events, SHARE |
| JEL: | D90 D91 D81 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2019:01&r=all |
| By: | Pietro Veronesi |
| Abstract: | I characterize a dynamic economy under general distributions of households’ risk tolerance, endowments, and beliefs about long-term growth. As the economy expands and the stock market rises (a) the fraction of households with declining consumption-share increases; (b) the wealth-share of high risk-tolerant households increases; (c) richer households’ wealth display a higher CAPM beta; and (d) households’ portfolios change qualitatively. A log-utility investor for instance borrows in contractions but lends in expansions. Variations in uncertainty and expected growth generate trading volume due to risk sharing. Higher uncertainty increases stock prices, risk premiums, volatility, wealth inequality and the dispersion of portfolio holdings, consistently with the events in the late 1990s. |
| JEL: | E21 G1 G11 G12 |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:25448&r=all |
| By: | Demeze-Jouatsa, Ghislain-Herman (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | In this paper, we present a model of finitely repeated games in which players can strategically make use of objective ambiguity. In each round of a finite rep- etition of a finite stage-game, in addition to the classic pure and mixed actions, players can employ objectively ambiguous actions by using imprecise probabilistic devices such as Ellsberg urns to conceal their intentions. We find that adding an infinitesimal level of ambiguity can be enough to approximate collusive payoffs via subgame perfect equi- librium strategies of the finitely repeated game. Our main theorem states that if each player has many continuation equilibrium payoffs in ambiguous actions, any feasible pay- off vector of the original stage-game that dominates the mixed strategy maxmin payoff vector is (ex-ante and ex-post) approachable by means of subgame perfect equilibrium strategies of the finitely repeated game with discounting. Our condition is also necessary. |
| Keywords: | Objective Ambiguity, Ambiguity Aversion, Finitely Repeated Games, Subgame Perfect Equilibrium, Ellsberg Urns, Ellsberg Strategies |
| Date: | 2018–08–13 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:585&r=all |
| By: | Pierpaolo Battigalli; Roberto Corrao; Federico Sanna |
| Abstract: | We consider multi-stage games with incomplete information and observable actions, and we analyze strategic reasoning by means of epistemic events within a total state space made of all the pro les of behaviors (paths of play) and possibly incoherent in nite hierarchies of conditional beliefs. Thus, we do not rely on types structures, or similar epistemic models. Subjective rationality is de ned by the conjunction of coherence of belief hierarchies, rational planning, and consistency between plan and on-path behavior. Since consistent hierarchies uniquely induce beliefs about behavior and belief hierarchies of others, we can de ne rationality and common strong belief in rationality, and analyze their behavioral and low-order beliefs implications, which are characterized by strong rationalizability. Our approach allows to extend known techniques to the epistemic analysis of psychological games where the utilities of outcomes depend on beliefs of order k or lower. This covers almost all applications of psychological game theory. JEL Classification Numbers: C72, C73, D82. Keywords: Epistemic game theory, belief hierarchies, consistency, subjective rationality, strong rationalizability, psychological games. |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:igi:igierp:641&r=all |
| By: | Danielis, Romeo; Scorrano, Mariangela; Giansoldati, Marco; Rotaris, Lucia |
| Abstract: | We perform a meta-analysis of the studies that evaluate the importance attributed by the consumers to the driving range of the Battery Electric Vehicles (BEVs). The paper updates and extends the paper by Dimitropoulos et al. (2013), including primary studies up to the year 2018. It tests whether the conclusions drawn by Dimitropoulos et al. (2013) still hold true given the many changes that occurred in the last years concerning BEVS’ uptake in the market, growing consumers’ direct and indirect experience with electric cars, vehicles’ increased range, and growing diffusion of the charging infrastructure. We carried out two analyses: a) the estimation of the summary effect size of the driving range utility coefficient, and b) a meta-regression of the willingness to pay for a 1-km increase in the BEVs’ driving range. The main findings are that: a) the importance attributed to the BEV’s range by the consumers has not decreased; b) there is a very large dispersion of the estimates around the mean values, implying that there is a large heterogeneity due to differences in respondents’ needs, vehicle segments and modelling techniques. The meta-regression allowed us to further explore and test statistically these conclusions. |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:sit:wpaper:19_2&r=all |
| By: | Julio Backhoff-Veraguas; Daniel Bartl; Mathias Beiglb\"ock; Manu Eder |
| Abstract: | Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, she is left with the possibility that Q does not provide an exact description of reality. This leads us the following question: will the hedge still be somewhat meaningful for models in the proximity of Q? If we measure proximity with the usual Wasserstein distance (say), the answer is NO. Models which are similar wrt Wasserstein distance may provide dramatically different information on which to base a hedging strategy. Remarkably, this can be overcome by considering a suitable adapted version of the Wasserstein distance which takes the temporal structure of pricing models into account. This adapted Wasserstein distance is most closely related to the nested distance as pioneered by Pflug and Pichler. It allows us to establish Lipschitz properties of hedging strategies for semimartingale models in discrete and continuous time. Notably, these abstract results are sharp already for Brownian motion and European call options. |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1901.07450&r=all |
| By: | Yannick Gabuthy; Pierre-Henri Morand |
| Abstract: | Many jurisdictions in Europe foresee the opportunity to allow the use of pay-forperformance (outcome-based) contracts in lawyer-client relationships, via the socalled contingent/conditional fees. In this article, we analyze the welfare implications of such fee regimes – regarding their effects on litigation outcomes – by modeling the lawsuit as an auction. The criteria for regime comparison are litigation costs, lawyers’ profits, and parties’ incentives to reach a pre-trial settlement. The main result shows that switching from hourly to outcome-based fees may increase the trial costs and the lawyers’ profits, and enhance the likelihood of settlement (by decreasing the litigants’ expected utilities at trial). This last effect may challenge an important argument in favor of pay-for-performance contracts, that is the objective of promoting access to justice, which is an overriding public policy motivation behind the introduction of these remuneration systems. |
| Keywords: | Litigation expenditures, Pre-trial settlement, Legal fees. |
| JEL: | D44 K40 K41 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ulp:sbbeta:2019-03&r=all |