Non-expected Utility Preferences Research Articles

Hybrid decision model and the ranking of experiments

Departing from the reduction of compound lotteries axiom on multi-stage lotteries, this paper proposes a new hybrid model to analyze decision trees. Applied to multi-stage decision trees induced by experiments, Blackwell’s (1953) definition of the relation “more informative” on the set of information structures is equivalent to experiments being more valuable to a class of non-expected utility preferences. This result extends Blackwell’s theorem and provides new insights regarding the evaluation of information produced by experiments.

Value of life and annuity demand

AbstractHow 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 nonexpected 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 a 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.

Optimal Auctions: Non-expected Utility and Constant Risk Aversion

Abstract We study auction design for bidders equipped with non-expected utility preferences that exhibit constant risk aversion (CRA). The CRA class is large and includes loss-averse, disappointment-averse, mean-dispersion, and Yaari’s dual preferences as well as coherent and convex risk measures. Any preference in this class displays first-order risk aversion, contrasting the standard expected utility case which displays second-order risk aversion. The optimal mechanism offers “ full-insurance” in the sense that each agent’s utility is independent of other agents’ reports. The seller excludes less types than under risk neutrality and awards the object randomly to intermediate types. Subjecting intermediate types to a risky allocation while compensating them when losing allows the seller to collect larger payments from higher types. Relatively high types are willing to pay more, and their allocation is efficient.

A Generalization of Quantal Response Equilibrium via Perturbed Utility

We present a tractable generalization of quantal response equilibrium via non-expected utility preferences. In particular, we introduce concave perturbed utility games in which an individual has strategy-specific utility indices that depend on the outcome of the game and an additively separable preference to randomize. The preference to randomize can be viewed as a reduced form of limited attention. Using concave perturbed utility games, we show how to enrich models based on logit best response that are common from quantal response equilibrium. First, the desire to randomize can depend on opponents’ strategies. Second, we show how to derive a nested logit best response function. Lastly, we present tractable quadratic perturbed utility games that allow complementarity.

A Theory of Auctions with Endogenous Valuations

We derive the revenue maximizing allocation of m units among n symmetric agents who have unit demand, and who take costly actions that in uence their values before participating in the mechanism. The allocation problem with costly actions can be represented by a reduced form model where agents have convex, non-expected utility preferences over the interim probability of receiving an object. Both the uniform m+1 price auction and the discriminatory pay-your-bid auction with reserve price constitute symmetric revenue maximizing mechanisms. Contrasting the case with exogenous valuations, the optimal reserve price reacts to both demand and supply. We also identify a condition under which the optimal mechanism is indeed symmetric, and illustrate the structure of the optimal asymmetric mechanism when the condition fails. The main tool in our analysis is an integral inequality, due to Fan and Lorentz (1954), involving majorization, super-modularity and convexity.

Optimal Auctions for Dual Risk Averse Bidders: Myerson meets Yaari

We study auction design for bidders equipped with non-expected utility preferences that exhibit constant risk aversion (CRA). The CRA class is large and includes loss-averse, disappointment-averse, mean-dispersion and Yaari's dual preferences as well as coherent and convex risk measures. The optimal mechanism offers full-insurance in the sense that each agent's utility is independent of other agents' reports. The seller excludes less types than under risk neutrality, and awards the object randomly to intermediate types. Subjecting intermediate types to a risky allocation while compensating them when losing allows the seller to collect larger payments from higher types. Relatively high types are anyway willing to pay more, and their allocation is efficient. (A previous version has been circulated under the title Optimal Auctions for Dual Risk Averse Bidders: Myerson meets Yaari.)

The Relation between Behavior under Risk and over Time

The paper establishes a tight relation between nonstandard behaviors in the domains of risk and time, by considering a decision-maker with non-expected utility preferences who believes that only present consumption is certain while any future consumption is uncertain. We provide the first complete characterizations of the two-way relations between the certainty effect and present bias, and between the common ratio effect and temporal reversals. (JEL D11, D15, D81, D91)

A Generalization of Quantal Response Equilibrium via Perturbed Utility

We present a tractable generalization of quantal response equilibrium via non-expected utility preferences. In particular, we introduce concave perturbed utility games in which an individual has strategy-specific utility indices that depend on the outcome of the game and an additively separable preference to randomize. We generalize logit best responses in three directions. First, the desire to randomize can depend on opponents' strategies. Second, we show how to derive a nested logit best response function. Lastly, we present tractable quadratic perturbed utility games that allow complementarity.

A Theory of Auctions with Endogenous Valuations

We derive the revenue maximizing allocation of m units among n symmetric agents who have unit demand, and who take costly actions that influence their values before participating in the mechanism. The allocation problem with costly actions can be represented by a reduced form model where agents have convex, non-expected utility preferences over the interim probability of receiving an object. Both the uniform m+1 price auction and the discriminatory pay-your-bid auction with reserve price constitute symmetric revenue maximizing mechanisms. Contrasting the case with exogenous valuations, the optimal reserve price reacts to both demand and supply. We also identify a condition under which the optimal mechanism is indeed symmetric, and illustrate the structure of the optimal asymmetric mechanism when the condition fails. The main tool in our analysis is an integral inequality, due to Fan and Lorentz (1954), involving majorization, super-modularity and convexity.

Value of Life and Annuity Demand

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.

Risk Taking and Fiscal Smoothing with Sovereign Wealth Funds in Advanced Economies

In an economy with a sovereign wealth fund (SWF), the government may draw on the fund to supplement other government revenues. If the fund is invested in risky assets, this introduces a new stochastic element into the government’s budget. We analyze the interaction between the draw from and risk taking in the SWF. Using non-expected utility preferences, we distinguish between intended changes and stochastic changes in the SWF draws over time. We show that the desire for smoothness in taxes and public services translates into smoothing of SWF draws and lower risk taking. It can even lead to procyclical rebalancing of the SWF portfolio. Future interest rates are associated with interest-rate risk. We show that this risk may lead to a higher optimal equity share in the SWF portfolio. Policy makers can use the draws from the SWF to smooth over time variation in risk-free rates.

Stochastic Dominance Analysis Without the Independence Axiom

We characterize the consistency of a large class of nonexpected utility preferences (including mean-variance preferences and prospect theory preferences) with stochastic orders (for example, stochastic dominances of different degrees). Our characterization rests on a novel decision theoretic result that provides a behavioral interpretation of the set of all derivatives of the functional representing the decision maker’s preferences. As an illustration, we consider in some detail prospect theory and choice-acclimating preferences, two popular models of reference dependence under risk, and we show the incompatibility of loss aversion with prudence. This paper was accepted by James Smith, decision analysis.

Cautious and Globally Ambiguity Averse

I study ambiguity attitudes in Uzi Segal's recursive non-expected utility model. I show that according to this model, the negative certainty independence axiom over simple lotteries is equivalent to a robust, or global form of ambiguity aversion that requires ambiguity averse behavior irrespective of the number of states and the decision maker's second-order belief. Thus, the recursive cautious expected utility model is the only subclass of Segal's model that robustly predicts ambiguity aversion. Similarly, the independence axiom over lotteries is equivalent to a robust form of ambiguity neutrality. In fact, any non-expected utility preference over lotteries coupled with a suitable second-order belief over three states produces either the Ellsberg paradox or the opposite mode of behavior. Finally, I propose a definition of a mean-preserving spread for second-order beliefs that is equivalent to increasing ambiguity aversion for every recursive preference that satisfies the negative certainty independence axiom.

Timing the stock market: Does it really make no sense?

Many private and institutional investors attempt to time the market and generate abnormal returns by periodically switching their portfolio allocations between the stock market and the cash market based on their return predictions. However, most academic studies emphasize that a successful market timing strategy requires a prediction accuracy that is usually not observable in reality. While prior studies evaluate the outcomes based on traditional return and risk measures, we adopt both expected and non-expected utility models to compare market timing with common benchmarks. Our analyses are based on a “simulated market timer” that does not require a specific forecast model. Bootstrap-based simulations show that even with low hit ratios, investors with non-expected utility preferences can consider market timing as highly desirable. The attractiveness of market timing is also partly attributable to short-termism in performance evaluation.

Harsanyi’s theorem without the sure-thing principle: On the consistent aggregation of Monotonic Bernoullian and Archimedean preferences

This paper studies the extension of Harsanyi’s theorem (Harsanyi, 1955) in a framework involving uncertainty. It seeks to extend the aggregation result to a wide class of Monotonic Bernoullian and Archimedean preferences (Cerreia-Vioglio et al., 2011) that subsumes many models of choice under uncertainty proposed in the literature. An impossibility result is obtained, unless we are in the specific framework where all individuals and the social observer are subjective expected utility maximizers sharing the same beliefs. This implies that non-expected utility preferences cannot be aggregated consistently.

Eliciting subjective probabilities with binary lotteries

We evaluate a binary lottery procedure for inducing risk neutral behavior in a subjective belief elicitation task. Prior research has shown this procedure to robustly induce risk neutrality when subjects are given a single risk task defined over objective probabilities. Drawing a sample from the same subject population, we find evidence that the binary lottery procedure also induces linear utility in a subjective probability elicitation task using the Quadratic Scoring Rule. We also show that the binary lottery procedure can induce direct revelation of subjective probabilities in subjects with popular non-expected utility preference representations that satisfy weak conditions.

Stability of risk preference measures: results from a field experiment on French farmers

We compare two different elicitation methods for measuring risk attitudes on a sample of French farmers. We consider the lottery tasks initially proposed by Holt and Laury (Econ Rev 92:1644–1655, 2002) and by Eckel and Grossman (Evol Hum Behav 23:281–295, 2002; J Econ Behav Org 68:1–7, 2008). The main empirical result from this within-subject study is that risk preference measures are affected by the type of mechanism used. We first show that this risk preference instability can be related to non-expected utility preferences of farmers. Using a risk-taking psychometric questionnaire, we then demonstrate that risk preferences of farmers are context-dependent. This may be another explanation of the observed risk preference instability.

Core and equilibria under ambiguity

This paper introduces new core and Walrasian equilibrium notions for an asymmetric information economy with non-expected utility preferences. We prove existence and incentive compatibility results for the notions we introduce. We also discuss a framework for ex ante, interim and ex post preferences.

Dynamic consistency for non-expected utility preferences

This paper considers a generalization of the Savage framework in which there are two state spaces as follows: one to model events and one to define acts. The distinction between these two spaces typically induces non-consequentialist motives. The dynamic derivation of the Sure Thing Principle is studied in this framework. When these two spaces are substantially different, there exists a class of preferences that satisfy dynamic consistency and, at the same time, rationalize violations of the Sure Thing Principle. Consequently, it is possible to use non-expected utility preferences to study problems with dynamic consistency, as long as preferences belong to the previous class and as long as problems refer to information structures, defined as partitions over the set that serves to model events.

Preferences for One-Shot Resolution of Uncertainty and Allais-Type Behavior, Second Version

Experimental evidence suggests that individuals are more risk averse when they perceive risk that is gradually resolved over time. We address these findings by studying a decision maker (DM) who has recursive, non-expected utility preferences over compound lotteries. DM has preferences for one-shot resolution of uncertainty (PORU) if he always prefers any compound lottery to be resolved in a single stage. We establish an equivalence between dynamic PORU and static preferences that are identified with commonly observed behavior in Allais-type experiments. The implications of this equivalence on preferences over information systems are examined. We define the gradual resolution premium and demonstrate its magnifying effect when combined with the usual risk premium. In an intertemporal context, PORU captures loss aversion with narrow framing.