nep-upt New Economics Papers
on Utility Models and Prospect Theory
Issue of 2021‒05‒03
twenty-two papers chosen by
Alexander Harin
Modern University for the Humanities

  1. Utility Representation in Abstract Wiener Space By Charles-Cadogan, G.
  2. Value of Life and Annuity Demand By Pashchenko, Svetlana; Porapakkarm, Ponpoje
  3. Top Down or Bottom Up? Disentangling the Channels of Attention in Risky Choice By Jan Engelmann; Alejandro Hirmas; Joël van der Weele
  4. Decision Making under Uncertainty: An Experimental Study in Market Settings By Echenique, Federico; Imai, Taisuke; Saito, Kota
  5. Ergodicity transformation for additive-ruin wealth dynamic By Carlos Rodríguez Raposo; Pablo Coello Pulido
  6. Fighting Fire with Fire - Overcoming Ambiguity Aversion by Introducing more Ambiguity By Dirk van Straaten; René Fahr
  7. Objective Rationality Foundations for (Dynamic) α-MEU By Frick, Mira; Iijima, Ryota; Le Yaouanq, Yves
  8. Fully Bayesian Aggregation By Franz Dietrich
  9. Intertemporal Preferences and the Adoption Decision for Bluetooth Speakers By Guhl, Daniel; Klapper, Daniel
  10. An Empirical Assessment of Characteristics and Optimal Portfolios By Christopher G. Lamoureux; Huacheng Zhang
  11. "Portfolio Optimization with Choice of a Probability Measure" By Taiga Saito; Akihiko Takahashi
  12. Student Performance and Loss Aversion By Karle, Heiko; Engelmann, Dirk; Peitz, Martin
  13. Rational vs. irrational beliefs in a complex world By Böhl, Gregor; Hommes, Cars H.
  14. Where to Refuel: Modeling On-the-way Choice of Convenience Outlet By Ari Pramono; Harmen Oppewal
  15. Coupled Lotteries – A New Method to Analyze Inequality Aversion By Koch, Melanie; Menkhoff, Lukas; Schmidt, Ulrich
  16. On the Causes and Consequences of Deviations from Rational Behavior By Strittmatter, Anthony; Sunde, Uwe; Zegners, Dainis
  17. Limited Impact of Business Development Programs on Profitability in the Presence of Ambiguity Aversion By Shapiro, Dmitry
  18. Bargaining for Community Fishing Quotas By Asproudis, Elias; Filippiadis, Eleftherios
  19. Repeated Games with Endogenous Discounting By Kochov, Asen; Song, Yangwei
  20. School Choice and Loss Aversion By Meisner, Vincent; von Wangenheim, Jonas
  21. On the Optimal Reform of Income Support for Single Parents By Ortigueira, Salvador; Siassi, Nawid
  22. Risky Gravity By Luciana Juvenal; Paulo Santos Monteiro

  1. By: Charles-Cadogan, G. (University of Leicester)
    Abstract: We extend Machina’s (1982) preference functional to abstract Wiener space. This has the advantage of extending utility functions to: infinite dimensional spaces; providing estimates for Machina’s (1982) nonlinear utility functional; and establishing a nexus between microfoundations of local utility, subjective probability, prospect theory, and elements of quantum decision theory without complex valued Hilbert spaces. For example, the class of Markowitz nonconvex utility functions (for which prospect theory’s value function is a special case) are vector valued functions in abstract Wiener space. Instead of preferences over probability distributions, the problem is transformed into one of preferences over states. Under Arzela-Ascoli Theorem, Wiener measure is the limit and unique conjugate prior in Wiener space. By a change of measure local subjective (posterior) probability is a Wiener integral. So, binary choice is stochastic. This poses a challenge for the transitivity axiom because intransitive preferences will occur in that space almost surely. Savage’s (1972) SEU fails in the space because probability is state dependent. JEL codes: C02 ; D81
    Keywords: decision theory ; local utility ; nonlinear subjective probability ; abstract Wiener spaces
    Date: 2021
  2. By: Pashchenko, Svetlana; Porapakkarm, Ponpoje
    Abstract: How does the value of life affect annuity demand? To address this question, we construct a portfolio choice problem with three key features: i) agents have access to life-contingent assets, ii) they always prefer living to dying, iii) agents have non-expected utility preferences. We show that as utility from being alive increases, annuity demand decreases (increases) if agents are more (less) averse to risk rather than to intertemporal fluctuations. Put differently, if people prefer early resolution of uncertainty, they are less interested in annuities when the value of life is high. Our findings have two important implications. First, we get better understanding of the well-known annuity puzzle. Second, we argue that the observed low annuity demand provides evidence that people prefer early rather than late resolution of uncertainty.
    Keywords: annuities, value of a statistical life, portfolio choice problem, life-contingent assets, longevity insurance
    JEL: D91 G11 G22
    Date: 2021–04–15
  3. By: Jan Engelmann (University of Amsterdam); Alejandro Hirmas (University of Amsterdam); Joël van der Weele (University of Amsterdam)
    Abstract: Economists have become increasingly interested in using attention to explain behavioral patterns both on the micro and macro level. This has resulted in several disparate theoretical approaches. Some, like rational inattention, assume a “top-down†model of executive optimization. Others, like salience theory, assume a “bottom-up†influence where attention is driven by contextual factors. This distinction is fundamental for the economic implications of attention, but so far there is little understanding of their relative importance. We propose a multi-attribute random utility model that unifies prior theoretical approaches by distinguishing between the impact of top-down and bottom-up attention. We accomplish this by separating agent-specific and decision-specific variation in attention and verify our framework in an eye-tracking experiment on risky choice. We find that both top-down and bottom-up attention are connected to important choice variables: both are associated with the weighting of the attributes of choice options, while top-down attention is additionally associated with measures of loss aversion. We discuss the insights regarding the nature of attention and its role in economic theory.
    Keywords: Attention, Random, Utility Models, Eye-tracking, Loss Aversion
    JEL: D81 D83 D87 D91
    Date: 2021–04–26
  4. By: Echenique, Federico (California Institute of Technology); Imai, Taisuke (LMU Munich); Saito, Kota (California Institute of Technology)
    Abstract: We design and implement a novel experimental test of subjective expected utility theory and its generalizations. Our experiments are implemented in the laboratory with a student population, and pushed out through a large-scale panel to a general sample of the US population. We find that a majority of subjects’ choices are consistent with maximization of some utility function, but not with subjective utility theory. The theory is tested by gauging how subjects respond to price changes. A majority of subjects respond to price changes in the direction predicted by the theory, but not to a degree that makes them fully consistent with subjective expected utility. Surprisingly, maxmin expected utility adds no explanatory power to subjective expected utility. Our findings remain the same regardless of whether we look at laboratory data or the panel survey, even though the two subject populations are very different. The degree of violations of subjective expected utility theory is not affected by age nor cognitive ability, but it is correlated with financial literacy.
    Keywords: uncertainty; subjective expected utility; maxmin expected utility; revealed preference;
    JEL: D01 D81 D90
    Date: 2019–11–07
  5. By: Carlos Rodríguez Raposo (OpSeeker Tech SL); Pablo Coello Pulido (OpSeeker Tech SL)
    Abstract: Ergodicity economics provides a framework to derive utility functions that assure growth optimality without entering into subjective or psychological considerations. For additive wealth dynamics the utility function is linear. This implies risk neutrality and contrasts with empirical evidence that shows risk aversion for decision makers. In this article we derive the utility function for the additive-ruin dynamic, which is a modified additive dynamic that includes a ruin state. As in ruin theory, we define a wealth level under which the agent is considered to be ruined. Furthermore, like in the model of parisian ruin, we consider the agent to be ruined as long as she does not recover with time. The obtained utility is a linear plus exponential function which has already been studied in economic theory. Unlike in the pure additive case, we show that ergodicity economics predicts risk averse behavior for agents in the additive-ruin dynamic. This result gives an explanation to why agents might refuse positive expected value lotteries for some levels of wealth and not for others without having to make subjective hypothesis about the agent.
    Keywords: ergodicity economics,utility function,additive dynamics,ruin theory
    Date: 2021–04–14
  6. By: Dirk van Straaten (Paderborn University); René Fahr (Paderborn University)
    Abstract: Ambiguity aversion guides decision makers to choose a risky rather than an ambiguous prospect, a pattern that is not always beneficial. For example, even nowadays, private pensions often build on savings accounts, which are risky prospects with known probabilities, instead of stocks as the former ensure safe returns with fixed interest rates. In comparison, expected returns of stocks, which are ambiguous prospects with unknown probabilities, are significantly higher. This study aims at facilitating a better understanding of ambiguity aversion and suggests measures to improve decision-making. In our experiment, subjects are confronted with either decisions under risk or decisions under ambiguity. Controlling for risk attitudes, we estimate category weights in both domains and find significant differences, which indicate the present of ambiguity aversion. Contrary to our predictions on the amplifying effect of multiple sources of ambiguity, we find that category weights of ambiguity and risk converge each other when a second source of ambiguity is implemented. That is, we point out another option to deal with ambiguity when people have to choose between risky and ambiguous prospects. Instead of minimizing ambiguity, the introduction of a second source of ambiguity might help to compare alternatives with less biases through ambiguity aversion.
    Keywords: Unknown source credibility, Risk, Ambiguity aversion, Uncertainty, Customer ratings
    JEL: C91 D01 D81
    Date: 2021–04
  7. By: Frick, Mira (Yale University); Iijima, Ryota (Yale University); Le Yaouanq, Yves (LMU Munich)
    Abstract: We show how incorporating Gilboa, Maccheroni, Marinacci, and Schmeidler’s (2010) notion of objective rationality into the α-MEU model of choice under ambiguity (Hurwicz, 1951) can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference ≥^, which captures the complete ranking over acts the DM expresses when forced to make a choice; in addition, we endow the DM with a (possibly incomplete) objectively rational preference ≥*, which captures the rankings the DM deems uncontroversial. Under the objectively founded α-MEU model, ≥^ has an α-MEU representation and ≥* has a unanimity representation à la Bewley (2002), where both representations feature the same utility index and set of beliefs. While the axiomatic foundations of the baseline α-MEU model are still not fully understood, we provide a simple characterization of its objectively founded counterpart. Moreover, in contrast with the baseline model, the model parameters are uniquely identified. Finally, we provide axiomatic foundations for prior-by-prior Bayesian updating of the objectively founded α-MEU model, while we show that, for the baseline model, standard updating rules can be ill-defined.
    Keywords: ambiguity; α-MEU; objective rationality; updating;
    Date: 2020–07–27
  8. By: Franz Dietrich (CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)
    Abstract: Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, but achieves only static rationality. Our characterisation of linear-geometric preference aggregation has two corollaries: a characterisation of linear aggregation of values (Harsanyi's Theorem) and a characterisation of geometric aggregation of beliefs.
    Keywords: rational group agent,uncertainty,preference aggregation,opinion pooling,values aggregation,static versus dynamic rationality,expected-utility hypothesis,Bayesianism,group rationality versus Paretianism,spurious unanimity,ex-ante versus ex-post Pareto
    Date: 2021
  9. By: Guhl, Daniel (HU Berlin); Klapper, Daniel (HU Berlin)
    Abstract: The adoption decision for durable goods is intertemporal by definition. However, estimating utility and discount functions from revealed preference data using dynamic discrete choice models is difficult because of an inherent identification problem. To overcome this issue, we use stated preference data. Specifically, we employ the experimental design of Dubé, Hitsch, and Jindal (2014), where future prices are known and that elicits intertemporal adoption decisions for Bluetooth speakers in a discrete choice framework. We estimate several models of discounting (e.g., static, myopic, geometric, and quasi-hyperbolic) and find considerably lower discount factors than typical market interest rates would suggest. The values are also smaller compared to respondents’ matching-based discount factors, even though the correlation is positive and significant. Furthermore, there are substantial differences in discounting across respondents (i.e., heterogeneity in time-preferences) and lastly, there is no strong empirical evidence for quasi-hyperbolic discounting. Thus, the standard economic model seems to be appropriate for the data at hand.
    Keywords: intertemporal preferences; dynamic discrete choice models; durable goods adoption;
    JEL: C35 D9 D12 M31
    Date: 2019–12–13
  10. By: Christopher G. Lamoureux; Huacheng Zhang
    Abstract: We analyze characteristics' joint predictive information through the lens of out-of-sample power utility functions. Linking weights to characteristics to form optimal portfolios suffers from estimation error which we mitigate by maximizing an in-sample loss function that is more concave than the utility function. While no single characteristic can be used to enhance utility by all investors, conditioning on momentum, size, and residual volatility produces portfolios with significantly higher certainty equivalents than benchmarks for all investors. Characteristic complementarities produce the benefits, for example momentum mitigates overfitting inherent in other characteristics. Optimal portfolios' returns lie largely outside the span of traditional factors.
    Date: 2021–04
  11. By: Taiga Saito (Faculty of Economics, The University of Tokyo); Akihiko Takahashi (Faculty of Economics, The University of Tokyo)
    Abstract: This paper considers a new problem for portfolio optimization with a choice of a probability measure, particularly an optimal investment problem under sentiments. Firstly, we formulate the problem as a sup-sup-inf problem consisting of optimal investment and a choice of a probability measure expressing aggressive and conservative attitudes of the investor. Secondly, we obtain an expression of the volatility process of a backward stochastic differential equation related to the conservative sentiment in order to investigate cases where the sup-sup-inf problem is solved. Specifically, we take a Malliavin calculus approach to solve the problem and obtain an optimal portfolio process. Finally, we provide an expression of the optimal portfolio under the sentiments in two examples with stochastic uncertainties in an exponential utility case and investigate the impact of the sentiments on the portfolio process.
    Date: 2021–04
  12. By: Karle, Heiko (Frankfurt School of Finance & Management); Engelmann, Dirk (HU Berlin); Peitz, Martin (University of Mannheim)
    Abstract: In this paper, we match data on student performance in a multiple-choice exam with data on student risk preferences that are extracted from a classroom experiment. We find that more-loss-averse students leave more questions unanswered and perform worse in the multiple-choice exam when giving an incorrect answer is penalized compared to not answering. We provide evidence that loss aversion parameters extracted from lottery choices in a controlled experiment have predictive power in a field environment of decision making under uncertainty. Furthermore, the degree of loss aversion appears to be persistent over time, as the experiment was conducted three months prior to the exam. We also find important differences across genders; they are partly explained by differences in loss aversion.
    Keywords: loss aversion; decision making under uncertainty; multiple choice;
    JEL: C91 D01 D11 D83
    Date: 2019–09–16
  13. By: Böhl, Gregor; Hommes, Cars H.
    Abstract: Can boundedly rational agents survive competition with fully rational agents? The authors develop a highly nonlinear heterogeneous agents model with rational forward looking versus boundedly rational backward looking agents and evolving market shares depending on their relative performance. Their novel numerical solution method detects equilibrium paths characterized by complex bubble and crash dynamics. Boundedly rational trend-extrapolators amplify small deviations from fundamentals, while rational agents anticipate market crashes after large bubbles and drive prices back close to fundamental value. Overall rational and non-rational beliefs co-evolve over time, with time-varying impact, and their interaction produces complex endogenous bubble and crashes, without any exogenous shocks.
    Keywords: Heterogeneous agents,trend-extrapolation,bubbles,numerical solution method
    JEL: C63 E03 E32 E44 E51
    Date: 2021
  14. By: Ari Pramono; Harmen Oppewal
    Abstract: This paper introduces on-the-way choice of retail outlet as a form of convenience shopping. It presents a model of on-the-way choice of retail outlet and applies the model in the context of fuel retailing to explore its implications for segmentation and spatial competition. The model is a latent class random utility choice model. An application to gas station choices observed in a medium-sized Asian city show the model to fit substantially better than existing models. The empirical results indicate consumers may adopt one of two decision strategies. When adopting an immediacy-oriented strategy they behave in accordance with the traditional gravity-based retail models and tend to choose the most spatially convenient outlet. When following a destination-oriented strategy they focus more on maintaining their overall trip efficiency and so will tend to visit outlets located closer to their main destination and are more susceptible to retail agglomeration effects. The paper demonstrates how the model can be used to inform segmentation and local competition analyses that account for variations in these strategies as well as variations in consumer type, origin and time of travel. Simulations of a duopoly setting further demonstrate the implications.
    Date: 2021–04
  15. By: Koch, Melanie (DIW Berlin); Menkhoff, Lukas (HU and DIW Berlin); Schmidt, Ulrich (University of Kiel and ifW Kiel)
    Abstract: We develop and implement a new measure for inequality aversion: two peers are endowed with identical binary lotteries and the only choice they make is whether they want to play out the lotteries independently or with perfect positive correlation (coupling). Coupling has no other effect than preventing outcome inequality. We implement the method in a survey in rural Thailand as well as a supplemental sample in a lab in Germany. As theoretically expected, coupling is related to being more risk averse, to having social status concerns, and to relying more often on formal and informal insurance. However, coupling is not related to giving in the dictator game.
    Keywords: inequality aversion; correlated risk; social status concerns;
    JEL: D63 D91 D81
    Date: 2019–09–18
  16. By: Strittmatter, Anthony (University of St. Gallen); Sunde, Uwe (LMU Munich); Zegners, Dainis (Erasmus University Rotterdam)
    Abstract: This paper presents novel evidence for the prevalence of deviations from rational behavior in human decision making – and for the corresponding causes and consequences. The analysis is based on move-by-move data from chess tournaments and an identification strategy that compares behavior of professional chess players to a rational behavioral benchmark that is constructed using modern chess engines. The evidence documents the existence of several distinct dimensions in which human players deviate from a rational benchmark. In particular, the results show deviations related to loss aversion, time pressure, fatigue, and cognitive limitations. The results also demonstrate that deviations do not necessarily lead to worse performance. Consistent with an important influence of intuition and experience, faster decisions are associated with more frequent deviations from the rational benchmark, yet they are also associated with better performance.
    Keywords: Rational strategies; artificial intelligence; behavioral bias;
    JEL: D01 D9 C7 C8
    Date: 2020–05–29
  17. By: Shapiro, Dmitry (Seoul National University)
    Abstract: This paper develops a theoretical framework to explain the limited effect of business development programs (BDPs) on entrepreneurs’ profits. We argue that a mismatch between a BDP’s narrow focus on business-promoting strategies and the wider context in which microentrepreneurs operate can limit the impact of business training. In our framework, entrepreneurs are ambiguity averse and have multiple sources of income (e.g., business and wage incomes). We show that for a sufficiently ambiguity-averse entrepreneur with multiple income sources, efficient training can result in a decline in expected profit. Notably, when the wider context (multiple income sources, ambiguity aversion) is considered, the business training impact is limited and can result in a posttraining expected profit decline. This limited impact is caused by the diversifying role that the business income plays in household finances.
    Keywords: ambiguity aversion; business development programs; microentrepreneurship
    JEL: D10 O12 O16
    Date: 2020–04–22
  18. By: Asproudis, Elias; Filippiadis, Eleftherios
    Abstract: This paper presents a model based on the Nash bargaining for fishing quotas and wages between fishing communities and vessels, focusing on two cases: (a) the fishing communities are not environmentally conscious and ignore the external damages caused by the fishing industry emissions, and (b) the fishing communities are environmentally conscious, and the external damages caused by the fishing industry emissions affect their bargaining position in the fishing quotas market. Between other it is argued that, in developing economies, where normally the Total Allowable Catch (TAC) is relatively strict compared to the community's needs, the community's degree of environmental awareness has no effect on social welfare. In developed countries the social welfare is higher when the fishing community is environmentally conscious provided a slow decrease in consumption's marginal utility relative to the rate at which the marginal environmental damage increases. Finally, the community's utility and the vessel's profits depend on the strictness of the total allowable catch.
    Keywords: bargaining, fishing quotas, environmental protection, fishing community, vessels, social welfare.
    JEL: C7 Q13 Q22 Q5
    Date: 2021–04–25
  19. By: Kochov, Asen (University of Rochester); Song, Yangwei (HU Berlin)
    Abstract: In a symmetric repeated game with standard preferences, there are no gains from intertemporal trade. In fact, under a suitable normalization of utility, the payoff set in the repeated game is identical to that in the stage game. We show that this conclusion may no longer be true if preferences are recursive and stationary, but not time separable. If so, the players’ rates of time preference are no longer fixed, but may vary endogenously, depending on what transpires in the course of the game. This creates opportunities for intertemporal trade, giving rise to new and interesting dynamics. For example, the efficient and symmetric outcome of a repeated prisoner’s dilemma may be to take turns defecting, even though the efficient and symmetric outcome of the stage game is to cooperate. A folk theorem shows that such dynamics can be sustained in equilibrium if the players are sufficiently patient.
    Keywords: repeated games; efficiency; folk theorems; endogenous discounting;
    Date: 2020–03–02
  20. By: Meisner, Vincent (TU Berlin); von Wangenheim, Jonas (FU Berlin)
    Abstract: Extensive evidence suggests that participants in the direct student-proposing deferred-acceptance mechanism (DSPDA) play dominated strategies. In particular, students with low priority tend to misrepresent their preferences for popular schools. To explain the observed data, we introduce expectationbased loss aversion into a school-choice setting and characterize choiceacclimating personal equilibria in DSPDA. Truthful equilibria can fail to exist, and DSPDA might implement unstable and more inefficient allocations in both small and large markets. Specifically, it discriminates against students who are more loss averse or less overconfident than their peers, and amplifies already existing (or perceived) discrimination. To level the playing field, we propose serial dictatorship mechanisms as a strategyproof and stable alternative that is robust to these biases.
    Keywords: market design; matching; school choice; reference-dependent preferences; loss aversion; deferred acceptance;
    JEL: C78 D78 D82 D81 D91
    Date: 2019–12–05
  21. By: Ortigueira, Salvador; Siassi, Nawid
    Abstract: We characterize the optimal reform of U.S. income support for low-income single parents. We develop a heterogeneous agents model with idiosyncratic risk and incomplete asset markets where single parents evolve through three life stages defined by their children's care needs. Using the U.S. tax-transfer system as the benchmark policy and a sample of single mothers drawn from the CPS, we assess reforms that maximize the expected utility of entering mothers. When policy cannot be tagged by the single mothers' life stage, the optimal reform calls for an increase in out-of-work income support by 11 percent, from $6,320 to $7,080, and a decrease in the wage subsidy to low-wage workers from 34 to 22 percent. This reform delivers substantial welfare gains for single mothers-to-be, and has the support of a vast majority of incumbent mothers. Tagging policy by the life stage makes the government's trade-off between providing insurance to single mothers in stage one (child in pre-schooling age) and incentivizing them to work when they transit to stage two (child in school age) more favorable, thus increasing their scope for smoothing marginal utility throughout life stages. Single mothers in stage one receive $8,950 in out-of-work support, and no subsidies to low-wages. For single mothers in stage two the optimal reform prescribes a reduction in out-of-work income support and an increase in work subsidies. Tagging brings additional welfare gains.
    Keywords: Optimal income transfers,Single-parent households,Intertemporal savings and labor supply
    JEL: D15 E21 E61
    Date: 2021
  22. By: Luciana Juvenal; Paulo Santos Monteiro
    Abstract: We consider the canonical trade model with heterogeneous firms, love for variety and trade costs, and integrate it in the consumption CAPM model. This yields a structural gravity equation that includes an additional factor related to risk premia. Empirical evidence based on firm-level data confirms the importance of cross-sectional heterogeneity in risk and time-varying risk premia to shape bilateral trade flows. The structural gravity model augmented to account for fluctuations in risk premia offers a compelling explanation for trade collapses during abrupt economic downturns.
    Keywords: Risk premia, Gravity equation, Trade collapse
    JEL: F12 F41 F44
    Date: 2021–04

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