The strength of sensitivity to ambiguity

We report an experiment where each subject’s ambiguity sensitivity is measured by an ambiguity premium, a concept analogous to and comparable with a risk premium. In our design, some tasks feature known objective risks and others uncertainty about which subjects have imperfect, heterogeneous, information (“ambiguous tasks”). We show how the smooth ambiguity model can be used to calculate ambiguity premia. A distinctive feature of our approach is estimation of each subject’s subjective beliefs about the uncertainty in ambiguous tasks. We find considerable heterogeneity among subjects in beliefs and ambiguity premia; and that, on average, ambiguity sensitivity is about as strong as risk sensitivity.     

Physician behavior and conditional altruism: the effects of payment system and uncertain health benefit

This paper experimentally investigates the altruistic behavior of physicians and whether this behavior is affected by payment system and uncertainty in health outcome. Subjects in the experiment take on the role of physicians and decide on the provision of medical care for different types of patients, who are identical in all respects other than the degree to which a given level of medical treatment affects their health. We investigate physician altruism from the perspective of ethical principles, by categorizing physicians according to how well their treatment decisions align with different principles for priority setting. The experiment shows that many physicians are altruistic toward their patients but also that the degree of altruism varies across patients with different medical needs. We find a strong effect of payment system that is overall unaffected by the introduction of risk and ambiguity in patients’ health outcomes. There is, however, substantial heterogeneity across individuals, in particular under the capitation payment system where physicians’ responses to the introduction of uncertainty in patient health are modulated by their own generic risk and ambiguity preferences.

     

Comparing risk preferences over financial and environmental lotteries

This paper investigates whether preferences over environmental risks are best modeled using probability-weighted utility functions or can be reasonably approximated by expected utility (EU) or subjective EU models as is typically assumed. I elicit risk attitudes in the financial and environmental domains using multiple-price list experiment. I examine how subjects?? behavioral, attitudinal, and demographic characteristics affect their probability weighting functions first for financial risks, then for oil-spill risks. I find that most subjects tend to overweight extreme positive outcomes relative to expected utility in both the environmental and financial domains. Subjects are more likely to overemphasize low probability, extreme environmental outcomes than low probability, extreme financial outcomes, leading subjects to offer more support for mitigating environmental gambles than financial gambles with the same odds and equivalent outcomes. I conclude that EU models are likely to underestimate subjects?? willingness to pay for environmental cleanup programs or policies with uncertain outcomes.     

Granny Versus Game Theorist: Ambiguity in Experimental Games

We report on an experiment in which subjects choose actions in strategic games with either strategic complements or substitutes against a granny, a game theorist or other subjects. The games are selected in order to test predictions on the comparative statics of equilibrium with respect to changes in strategic ambiguity. We find that subjects face higher ambiguity while playing against the granny than playing against the game theorist if we assume that subjects are ambiguity averse. Moreover, under the same assumption, subjects choose more secure actions in games more prone to ambiguity which is in line with the predictions.      

When Allais meets Ulysses: Dynamic axioms and the common ratio effect

We report experimental findings about subjects’ behavior in dynamic decision problems involving multistage lotteries with different timings of resolution of uncertainty. Our within-subject design allows us to study violations of the independence and dynamic axioms: Dynamic Consistency, Consequentialism and Reduction of Compound Lotteries. We investigate the effects of changes in probability and outcome levels on the pattern of choices observed in the Common Ratio Effect (CRE) and in the Reverse Common Ratio Effect (RCRE) and on their dynamic counterparts. We find that the probability level plays an important role in violations of Reduction of Compound Lottery and Dynamic Consistency and the outcomes levels in violations of Consequentialism. Moreover, more than one quarter of our subjects satisfy the Independence axiom but violate two dynamic axioms. We thus suggest that there is a greater dissociation that might have been expected between preferences captured by dynamic axioms and those observed over single-stage lotteries.     

Stake effects on ambiguity attitudes for gains and losses

We test the effect of stake size on ambiguity attitudes. Compared to a baseline condition, we find subjects to be more ambiguity seeking for small-probability gains and large-probability losses under high stakes. They are also more ambiguity averse for large-probability gains and small-probability losses. We trace these effects back to stake effects on decisions under risk (known probabilities) and uncertainty (unknown probabilities). For risk, we replicate previous findings. For uncertainty, we find an increase in probabilistic insensitivity under high stakes that is driven by increased uncertainty aversion for large-probability gains and for small-probability losses.     

Ambiguity aversion in multi-armed bandit problems

In multi-armed bandit problems, information acquired from experimentation is valuable because it tells the agent whether to select a particular option again in the future. This article tests whether people undervalue this information because they are ambiguity averse, or have a distaste for uncertainty about the average quality of each alternative. It is shown that ambiguity averse agents have lower than optimal Gittins indexes, appearing to undervalue information from experimentation, but are willing to pay more than ambiguity neutral agents to learn the true mean of the payoff distribution, appearing to overvalue objectively given information. This prediction is tested with a laboratory experiment that elicits a Gittins index and a willingness to pay on six two-armed bandits. Consistent with the predictions of ambiguity aversion, the Gittins indexes are significantly lower than optimal and willingnesses to pay are significantly higher than optimal.     

Recursive expected utility and the separation of attitudes towards risk and ambiguity: an experimental study

We use the multiple price list method and a recursive expected utility theory of smooth ambiguity to separate out attitude towards risk from that towards ambiguity. Based on this separation, we investigate if there are differences in agent behaviour under uncertainty over gain amounts vis-a-vis uncertainty over loss amounts. On an aggregate level, we find that (i) subjects are risk averse over gains and risk seeking over losses, displaying a “reflection effect” and (ii) they are ambiguity neutral over gains and are mildly ambiguity seeking over losses. Further analysis shows that on an individual level, and with respect to both risky and ambiguous prospects, there is limited incidence of a reflection effect where subjects are risk/ambiguity averse (seeking) in gains and seeking (averse) in losses, though this incidence is higher for ambiguous prospects. A very high proportion of such cases of reflection exhibit risk (ambiguity) aversion in gains and risk (ambiguity) seeking in losses, with the reverse effect being significantly present in the case of risk but almost absent in case of ambiguity. Our results suggest that reflection across gains and losses is not a stable individual characteristic, but depends upon whether the form of uncertainty is precise or ambiguous, since we rarely find an individual who exhibits reflection in both risky and ambiguous prospects. We also find that correlations between attitudes towards risk and ambiguity were domain dependent.      

Ambiguity aversion and familiarity bias: Evidence from behavioral and gene association studies

It is increasingly recognized that decision making under uncertainty depends not only on probabilities, but also on psychological factors such as ambiguity and familiarity. Using 325 Beijing subjects, we conduct a neurogenetic study of ambiguity aversion and familiarity bias in an incentivized laboratory setting. For ambiguity aversion, 49.4% of the subjects choose to bet on the 50–50 deck despite the unknown deck paying 20% more. For familiarity bias, 39.6% choose the bet on Beijing’s temperature rather than the corresponding bet with Tokyo even though the latter pays 20% more. We genotype subjects for anxiety-related candidate genes and find a serotonin transporter polymorphism being associated with familiarity bias, but not ambiguity aversion, while the dopamine D5 receptor gene and estrogen receptor beta gene are associated with ambiguity aversion only among female subjects. Our findings contribute to understanding of decision making under uncertainty beyond revealed preference.     

Anxiety and Decision Making with Delayed Resolution of Uncertainty

In many real-world gambles, a non-trivial amount of time passes before the uncertainty is resolved but after a choice is made. An individual may have a preference between gambles with identical probability distributions over final outcomes if they differ in the timing of resolution of uncertainty. In this domain, utility consists not only of the consumption of outcomes, but also the psychological utility induced by an unresolved gamble. We term this utility anxiety. Since a reflective decision maker may want to include anxiety explicitly in analysis of unresolved lotteries, a multiple-outcome model for evaluating lotteries with delayed resolution of uncertainty is developed. The result is a rank-dependent utility representation (e.g., Quiggin, 1982), in which period weighting functions are related iteratively. Substitution rules are proposed for evaluating compound temporal lotteries. The representation is appealing for a number of reasons. First, probability weights can be interpreted as the cognitive attention allocated to certain outcomes. Second, the model disaggregates strength of preference from temporal risk aversion and thus provides some insight into the old debate about the relationship between von Neumann–Morgenstern utility functions and strength of preference value functions.     

Evaluating second-order probability judgments with strictly proper scoring rules

Empirical studies have demonstrated that uncertainty about event probabilities, also known as ambiguity or second-order uncertainty, can affect decision makers choice preferences. Despite the importance of second-order uncertainty in decision making, almost no effort has been directed towards the development of methods that evaluate the accuracy of second-order probabilities. In this paper, we describe conditions under which strictly proper scoring rules can be used to assess the accuracy of second-order probability judgments. We investigate the effectiveness of using a particular strictly proper scoring rule the ranked probability score - to discourage biased assessments of second-order uncertainty.     

How much ambiguity aversion?

Experimental results on the Ellsberg paradox typically reveal behavior that is commonly interpreted as ambiguity aversion. The experiments reported in the current paper find the objective probabilities for drawing a red ball that make subjects indifferent between various risky and uncertain Ellsberg bets. They allow us to examine the predictive power of alternative principles of choice under uncertainty, including the objective maximin and Hurwicz criteria, the sure-thing principle, and the principle of insufficient reason. Contrary to our expectations, the principle of insufficient reason performed substantially better than rival theories in our experiment, with ambiguity aversion appearing only as a secondary phenomenon.     

An experimental investigation of imprecision attitude and its relation with risk attitude and impatience

We report in this article the result of three experiments on risk, ambiguity, and time attitude. The first two differed by the population considered (students vs. general population) while the third one used a different protocol and concerned students and portfolio managers. We find quite a lot of heterogeneity at the individual level. Of principal interest was the elicitation of risk, time, and ambiguity attitudes and the relationship among these (model free) measures. We find that on the student population, there is essentially no correlation. A non-negligible fraction of the population behaves in an extremely cautious manner in the risk and ambiguity domain. When we drop this population from the sample, the correlation between our measures is also non-significant. We also raise three questions linked to measurement of ambiguity attitudes that come out from our data sets.     

Learning-by-doing in an ambiguous environment

How well do revealed ambiguity preferences predict how people choose to seek new information about uncertain events? In an economics experiment, we apply a new instrument to measure ambiguity preferences, and in a later session observe to what extent the measure predicts the choice to receive costly information in a learning-by-doing game. Ambiguity averse subjects are more willing to pay to receive information, while risk averse subjects are not. Holding ambiguity preferences constant, risk averse subjects tend to perform worse than risk loving subjects. The returns to experimentation, especially for ambiguity averse subjects, suggest a not-well studied but important role that ambiguity preferences play in decision-making under uncertainty.     

Choice with imprecise information: an experimental approach

This article provides an experimental analysis of attitude toward imprecise and variable information. Imprecise information is provided in the form of a set of possible probability values, such that it is virtually impossible for the subjects to guess or estimate, which one in the set is true or more likely to be true. We investigate how geometric features of such information pieces affect choices. We find that the subjects care about more features than the pairs of best-case and worst-case, which is a counter-evidence to the well-known models, maximin and α-maximin. We find that presence of nonextreme points in the set affects choice, which suggests that attitude toward imprecision is ‘nonlinear.’ We also obtain an observation, though not significant, that information pieces have a complementarity that may not be explained by the Bayesian view.     

Is imprecise knowledge better than conflicting expertise? Evidence from insurers’ decisions in the United States

This paper reports the results of the first experiment in the United States designed to distinguish between two sources of ambiguity: imprecise ambiguity (expert groups agree on a range of probability, but not on any point estimate) versus conflict ambiguity (each expert group provides a precise probability estimate which differs from one group to another). The specific context is whether risk professionals (here, insurers) behave differently under risk (when probability is well-specified) and different types of ambiguity in pricing catastrophic risks (floods and hurricanes) and non-catastrophic risks (house fires). The data show that insurers charge higher premiums when faced with ambiguity than when the probability of a loss is well specified (risk). Furthermore, they tend to charge more for conflict ambiguity than imprecise ambiguity for flood and hurricane hazards, but less in the case of fire. The source of ambiguity also impacts causal inferences insurers make to reduce their uncertainty.     

Buying Insurance for Disaster-Type Risks: Experimental Evidence

This paper presents a series of experiments that confront subjects with low probability, high loss situations. A rich parameter set is examined and we find subjects respond to low probability, high loss risks in predictable ways. As loss events become more likely, or loss amounts get larger, or the cost of insurance falls, subjects are more likely to buy indemnifying insurance, even for the class of low probability risks that usually presents problems for standard expected utility theory. A novel application of Cameron's method to estimate willingness to pay from dichotomous choice responses allows us to estimate willingness to pay for insurance. We do not observe the bimodal distribution of bids found in other studies of similar risk situations.     

Coordination when there are restricted and unrestricted options

One might expect that, in pure coordination games, coordination would become less frequent as the number of options increases. Contrary to this expectation, we report an experiment which found more frequent coordination when the option set was unrestricted than when it was restricted. To try to explain this result, we develop a method for eliciting the general rules that subjects use to identify salient options in restricted and unrestricted sets. We find that each such rule, if used by all subjects, would generate greater coordination in restricted sets. However, subjects tend to apply different rules to restricted and unrestricted sets.     

Stochastic Dominance and Prospect Dominance with Subjective Weighting Functions

Laboratory experiments with and without real money repeatedly reveal that even if all subjects observe the same pair of cumulative distributions F and G, they act as if they were other cumulative probability functions F* and G* different for different investors. Namely, the subjects assign (subjective) weights to the various probabilities. In their breakthrough article Kahneman and Tversky [1979] suggest that in making decisions under uncertainty, the subjects apply a monotonic transformation (p) where p are the probabilities, and investors make decisions by comparing (p) corresponding to the two distributions under consideration rather than by comparing the true probabilities, p, themselves.