We provide a critical assessment of the ambiguity aversion literature, which we characterize in terms of the view that Ellsberg choices are rational responses to ambiguity, to be explained by relaxing Savage's Sure-Thing principle and adding an ambiguity-aversion postulate. First, admitting Ellsberg choices as rational leads to behaviour, such as sensitivity to irrelevant sunk cost, or aversion to information, which most economists would consider absurd or irrational. Second, we argue that the mathematical objects referred (...) to as “beliefs” in the ambiguity aversion literature have little to do with how an economist or game theorist understands and uses the concept. This is because of the lack of a useful notion of updating. Third, the anomaly of the Ellsberg choices can be explained simply and without tampering with the foundations of choice theory. These choices can arise when decision makers form heuristics that serve them well in real-life situations where odds are manipulable, and misapply them to experimental settings. (shrink)

The veil of ignorance argument was used by John C. Harsanyi to defend Utilitarianism and by John Rawls to defend the absolute priority of the worst off. In a recent paper, Lara Buchak revives the veil of ignorance argument, and uses it to defend an intermediate position between Harsanyi's and Rawls' that she calls Relative Prioritarianism. None of these authors explore the implications of allowing that agent's behind the veil are averse to ambiguity. Allowing for aversion to (...) class='Hi'>ambiguity---which is both the most commonly observed and a seemingly reasonable attitude to ambiguity---however supports a version of Egalitarianism, whose logical form is quite different from the theories defended by the aforementioned authors. Moreover, it turns out that the veil of ignorance argument neither supports standard Utilitarianism nor Prioritarianism unless we assume that rational people are insensitive to ambiguity. (shrink)

Coherent-ambiguity aversion is defined within the smooth-ambiguity model as the combination of choice-ambiguity and value-ambiguity aversion. Five ambiguous decision tasks are analyzed theoretically, where an individual faces two-stage lotteries with binomial, uniform, or unknown second-order probabilities. Theoretical predictions are then tested through a 10-task experiment. In tasks 1–5, risk aversion is elicited through both a portfolio choice method and a BDM mechanism. In tasks 6–10, choice-ambiguity aversion is elicited through the portfolio (...) choice method, while value-ambiguity aversion comes about through the BDM mechanism. The behavior of over 75 % of classified subjects is in line with the KMM model in all tasks 6–10, independent of their degree of risk aversion. Furthermore, the percentage of coherent-ambiguity-averse subjects is lower in the binomial than in the uniform and in the unknown treatments, with only the latter difference being significant. The most part of coherent-ambiguity-loving subjects show a high risk aversion. (shrink)

Daniel Ellsberg presented in Ellsberg (The Quarterly Journal of Economics 75:643–669, 1961) various examples questioning the thesis that decision making under uncertainty can be reduced to decision making under risk. These examples constitute one of the main challenges to the received view on the foundations of decision theory offered by Leonard Savage in Savage (1972). Craig Fox and Amos Tversky have, nevertheless, offered an indirect defense of Savage. They provided in Fox and Tversky (1995) an explanation of Ellsberg’s two-color problem (...) in terms of a psychological effect: ambiguity aversion . The ‘comparative ignorance’ hypothesis articulates how this effect works and explains why it is important to an understanding of the typical pattern of responses associated with Ellsberg’s two-color problem. In the first part of this article we challenge Fox and Tversky’s explanation. We present first an experiment that extends Ellsberg’s two-color problem where certain predictions of the comparative ignorance hypothesis are not confirmed. In addition the hypothesis seems unable to explain how the subjects resolve trade-offs between security and expected pay-off when vagueness is present. Ellsberg offered an explanation of the typical behavior elicited by his examples in terms of these trade-offs and in section three we offer a model of Ellsberg’s trade-offs. The model takes seriously the role of imprecise probabilities in explaining Ellsberg’s phenomenon. The so-called three-color problem was also considered in Fox and Tversky (1995). We argue that Fox and Tversky’s analysis of this case breaks a symmetry with their analysis of the two-color problem. We propose a unified treatment of both problems and we present a experiment that confirms our hypothesis. (shrink)

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. (shrink)

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. (shrink)

Clinical trials of novel agents often present several layers of ethical challenge. Because time and resources for ethical and safety review are limited, how investigators, IRBs, and regulators allocate attention to a trial's various safety dimensions itself represents a critical ethical question. In what follows, I use the example of a Parkinson's disease gene transfer trial to show how risks involving unknown probabilities or outcomes (ambiguity), might sometimes draw attention away from risks that involve known probabilities or outcomes. This (...) potentially undermines the goal of ‘systematic and nonarbitrary analysis of risk’ during ethical review. To counteract the possible effects of such attention biases, I propose that reviewers develop ‘cognitive aids’ like lists and, where appropriate, set aside time to discuss non-ambiguous risks. I also propose further research for addressing and understanding how attention allocation, emotion, and ambiguity influence ethical decision-making. (shrink)

Maximum-likelihood updating is a well-known approach for extending static ambiguity sensitive preferences to dynamic set-ups. This paper develops an example in which MLU induces an ambiguity averse maxmin expected utility decision-maker to prefer a bet on an ambiguous over a risky urn and be more willing to bet on the ambiguous urn compared to an subjective expected utility decision-maker. This is challenging, since prior to observing draws from the urns, the MEU decision-maker actually preferred the risky over the (...) ambiguous bet and was less willing to bet on the ambiguous urn than the SEU decision-maker. The identified switch in betting preferences is not due to a violation of dynamic consistency or consequentialism. Rather, it results from MLU’s selection of extreme priors, causing a violation of the stability of set inclusion over the course of the updating process. (shrink)

This article presents the results of a survey designed to test, with economically sophisticated participants, Ellsberg’s ambiguity aversion hypothesis, and Smithson’s conflict aversion hypothesis. Based on an original sample of 78 professional actuaries (all members of the French Institute of Actuaries), this article provides empirical evidence that ambiguity (i.e. uncertainty about the probability) affect insurers’ decision on pricing insurance. It first reveals that premiums are significantly higher for risks when there is ambiguity regarding the probability (...) of the loss. Second, it shows that insurers are sensitive to sources of ambiguity. The participants indeed, charged a higher premium when ambiguity came from conflict and disagreement regarding the probability of the loss than when ambiguity came from imprecision (imprecise forecast about the probability of the loss). This research thus documents the presence of both ambiguity aversion and conflict aversion in the field of insurance, and discuses economic and psychological rationales for the observed behaviours. (shrink)

The phenomenon of ambiguity aversion, in which risky gambles with known probabilities are preferred over ambiguous gambles with unknown probabilities, has been thoroughly documented in adults but never measured in children. Here, we use two distinct tasks to investigate ambiguity preferences of children (8- to 9-year-olds) and a comparison group of adults (19- to 27-year-olds). Across three separate measures, we found evidence for significant ambiguity aversion in adults but not in children and for greater (...) class='Hi'>ambiguity aversion in adults compared to children. As ambiguity aversion in adults has been theorized to result from a preference to bet on the known and avoid the unfamiliar, we separately measured familiarity bias and found that children, like adults, are biased towards the familiar. Our findings indicate that ambiguity aversion emerges across the course of development between childhood and adolescence, while a familiarity bias is already present in childhood. (shrink)

Optimal protective responses to long-term risks depend on rational perceptions of ambiguous risks and uncertain time horizons. Our study examined the joint influence of uncertain delay and risk in an original sample of business owners and managers. We found that many subjects disliked uncertainty in the timing of an outcome, a reaction we term ``lottery timing risk aversion.'' Such aversion to uncertain timing was positively related to aversion to ambiguous probabilities for lotteries involving storm damage risks. This (...) association suggests that uncertainty may be processed similarly in both the risk and time dimensions. (shrink)

The usage of imprecise probabilities has been advocated in many domains: A number of philosophers have argued that our belief states should be “imprecise” in response to certain sorts of evidence, and imprecise probabilities have been thought to play an important role in disciplines such as artificial intelligence, climate science, and engineering. In this paper I’m interested in the question of whether the usage of imprecise probabilities can be given a practical motivation (a motivation based on practical rather than epistemic, (...) or alethic concerns). My aim is to challenge the central motivation for using imprecise probabilities in decision-making that has been offered in the literature: the idea that, in at least some contexts, it’s desirable to be ambiguity averse. If I succeed, this will show that we need to reconsider whether there are good reasons to use imprecise probabilities in contexts in which making good decisions is what's of primary concern. (shrink)

The pioneering contributions of Bewley, Gilboa and Schmeidler highlighted important weaknesses in the foundations of economics and game theory. The Bayesian methodology on which these fields are based does not answer such basic questions as what makes beliefs reasonable, or how agents should form beliefs and expectations. Providing the initial impetus for debating these issues is a contribution that will have the lasting value it deserves.

Asymmetric Choquet random walks are defined, in the form of dynamically consistent random walks allowing for asymmetric conditional capacities. By revisiting Kast and Lapied and Kast et al. we show that some findings regarding the effects of ambiguity aversion are preserved in the more general framework, which is of interest in several applications to policy making, risk management, corporate decisions, real option valuation of investment/ disinvestment projects, etc. The effect of ambiguity on the higher moments is investigated, (...) as well, as they have an interpretation in terms of the psychological attitude of a decision-maker towards ambiguity. Finally, some financial applications are provided as an illustration. (shrink)

This paper proposes a notion of ambiguity aversion and characterizes it in the context of biseparable preferences, which include many popular ambiguity models in the literature. The defined properties suggest that ambiguity aversion is characterized by the properties of its capacity. This formalizes a sharp distinction between ambiguity and risk aversion, where risk aversion is characterized by the properties of its utility index and its probability weighting function.

Most decision-making research in economics focuses on individual decisions. Yet, we know, from psychological research in particular, that individual preferences can be sensitive to social pressures. In this paper, we study the impact of a group environment on individual preferences for risky and ambiguous prospects. In our experiment, each participant was invited to make a series of lottery-choice decisions in two different conditions. In the Alone condition, individuals made private choices, whereas in the Group condition, individuals belonged to a three-person (...) group and group members’ choices were aggregated according to either a majority or unanimity rule. This design allows us to study the impact of a group environment on individuals’ attitude towards both risky and ambiguous prospects, while controlling for the decision rule used in the group. Our experimental results show that when individuals are in the Group condition, they tend to be less risk averse and more ambiguity averse than when they are not part of a group. Our experiment also suggests that the decision rule matters as it shows that these two trends tend to be stronger when the group implements a unanimity rule. Specifically, we found that individuals who belong to a group implementing a unanimity rule are significantly less risk averse than individuals who belong to a group that relies on the majority rule. We obtained a similar—but non-significant—result under ambiguity. (shrink)

We report the results of an experiment which investigates the impact of the manner in which likelihood information is presented to decision-makers on valuations assigned to lotteries. We find that subjects who observe representative sequences of outcomes attach higher valuations to lotteries than those who are given only a verbal description of a probability distribution. We interpret this in terms of a reduction in ambiguity about the possible lottery outcomes. These findings suggest that ambiguity aversion may be (...) a confounding factor in reported experimental violations of expected utility theory based on verbal descriptions of probability distributions. (shrink)

The paradigm for modelling decision-making under uncertainty has undoubtedly been the theory of Expected Utility, which was first developed by von Neumann and Morgenstern (1944) and later extended by Savage (1954) to the case of subjective uncertainty. The inadequacy of the theory of Subjective Expected Utility (SEU) as a descriptive theory was soon pointed out in experiments, most famously by Allais (1953) and Ellsberg (1961). The observed departures from SEU noticed by Allais and Ellsberg became known as “paradoxes”. The Ellsberg (...) paradox gave rise, several years later, to a new literature on decision-making under ambiguity. The theoretical side of this literature was pioneered by Schmeidler (1989). This literature views the departures from SEU in situations similar to those discussed by Ellsberg as rational responses to ambiguity. The rationality is “recovered” by relaxing Savage's Sure-Thing principle and adding an ambiguity-aversion postulate. Thus the ambiguity-aversion literature takes a normative point of view and does consider Ellsberg-type choices as behavioural “anomalies”. (shrink)

Several years ago, Cohen, Dearnaley, and Hansel [1] demonstrated that under the influence of alcohol drivers became more risk prone, although their risk perception remained unchanged. Research shows that ambiguity aversion is to some extent positively correlated with risk aversion, though not very highly [2]. The question addressed by the present research is whether alcohol reduces ambiguity aversion. Our research was conducted in a natural setting (a restaurant bar), where customers with differing levels of alcohol (...) intoxication were offered a choice between a risky and an ambiguous lottery. We found that alcohol reduced ambiguity aversion and that the effect occurred in men but not women. We interpret these findings in terms of the risk-as-value hypothesis, according to which, people in Western culture tend to value risk, and suggest that alcohol consumption triggers adherence to socially and culturally valued patterns of conduct different for men and women. (shrink)

Using a large sample of retail investors as well as experimental data we find that risk and ambiguity aversion are positively correlated. We provide evidence that a common link is decision mode: intuitive thinkers tolerate more risk and ambiguity than effortful reasoners. One interpretation is that intuitive thinking confers an advantage in risky or ambiguous situations. We present supporting lab and field evidence that intuitive thinkers outperform others in uncertain environments. Finally, we find that risk and (...) class='Hi'>ambiguity aversion vary with individual characteristics and wealth. The wealthy are less risk averse but more ambiguity averse, which has implications for financial puzzles. (shrink)

Prospect theory emerged as one of the leading descriptive decision theories that can rationalize a large body of behavioral regularities. The methods for eliciting prospect theory parameters, such as its value function and probability weighting, are invaluable tools in decision analysis. This paper presents a new simple method for eliciting prospect theory’s value function without any auxiliary/simplifying parametric assumptions. The method is applicable both to choice under ambiguity (Knightian uncertainty) and risk (when events are characterized by objective probabilities). Our (...) new elicitation method is implemented in a simple paper-and-pencil experiment (via an iterative multiple price list format). This is one of the first experiments that elicits non-parametric prospect theory’s value function with salient rewards. The collected data generally confirm findings in the existing literature: the value function is S-shaped (concave in the gain domain and convex in the loss domain) though there is a weaker loss aversion on the aggregate level and a substantial heterogeneity in loss aversion on the individual level (41% loss averse, 6% loss neutral and 53% gain seeking). (shrink)

Heath and Tversky (1991, Journal of Risk and Uncertainty 4:5–28) posed that reaction to ambiguity is driven by perceived competence. Competence effects may be inconsistent with ambiguity aversion if betting on own judgement is preferred to betting on a chance event, because judgemental probabilities are more ambiguous than chance events. This laboratory experiment analyses whether ambiguity affects prices and volumes in a double auction market, and contrasts ambiguity aversion to competence effects. In order to (...) test for the presence of competence effects, in the experiment uncertainty is tied to the realisation of events about which the decision maker is more or less knowledgeable. Two experiments are presented: in the first, knowledge is exogenous, whereas in the second the knowledge judgement is endogenous. Market prices provide evidence in favour of the competence hypothesis only when competence is self-assessed. Comparable volumes are observed in both experiments. (shrink)

We use probability-matching variations on Ellsberg’s single-urn experiment to assess three questions: (1) How sensitive are ambiguity attitudes to changes from a gain to a loss frame? (2) How sensitive are ambiguity attitudes to making ambiguity easier to recognize? (3) What is the relation between subjects’ consistency of choice and the ambiguity attitudes their choices display? Contrary to most other studies, we find that a switch from a gain to a loss frame does not lead to (...) a switch from ambiguity aversion to ambiguity neutrality and/or ambiguity seeking. We also find that making ambiguity easier to recognize has little effect. Finally, we find that while ambiguity aversion does not depend on consistency, other attitudes do: consistent choosers are much more likely to be ambiguity neutral, while ambiguity seeking is much more frequent among highly inconsistent choosers. (shrink)

Heath and Tversky (1991, Journal of Risk and Uncertainty 4:5–28) posed that reaction to ambiguity is driven by perceived competence. Competence effects may be inconsistent with ambiguity aversion if betting on own judgement is preferred to betting on a chance event, because judgemental probabilities are more ambiguous than chance events. This laboratory experiment analyses whether ambiguity affects prices and volumes in a double auction market, and contrasts ambiguity aversion to competence effects. In order to (...) test for the presence of competence effects, in the experiment uncertainty is tied to the realisation of events about which the decision maker is more or less knowledgeable. Two experiments are presented: in the first, knowledge is exogenous, whereas in the second the knowledge judgement is endogenous. Market prices provide evidence in favour of the competence hypothesis only when competence is self-assessed. Comparable volumes are observed in both experiments. (shrink)

Suppose we want to do the most good we can with a particular sum of money, but we cannot be certain of the consequences of different ways of making use of it. This article explores how our attitudes towards risk and ambiguity bear on what we should do. It shows that risk-avoidance and ambiguity-aversion can each provide good reason to divide our money between various charitable organizations rather than to give it all to the most promising one. (...) It also shows how different attitudes towards risk and ambiguity affect whether we should give to an organization which does a small amount of good for certain or to one which does a large amount of good with some small or unknown probability. (shrink)

In this paper, ambiguity aversion to uncertain survival probabilities is introduced in a static life-cycle model with a bequest motive to study the optimal demand for annuities. Provided that annuities’ return is sufficiently large, and notably when it is fair, positive annuitization is known to be the optimal strategy of ambiguity neutral individuals. Conversely, we show that the demand for annuities decreases with ambiguity aversion and that there exists a finite degree of aversion above (...) which the demand is non-positive: the optimal strategy is then to either sell annuities short or to hold zero annuities if the former option is not available. To conclude, ambiguity aversion appears to be a relevant candidate for explaining the annuity puzzle. (shrink)

There are few models of price competition in a homogeneous-good market which permit general asymmetries of information amongst the sellers. This work studies a price game with discontinuous payoffs in which both costs and market demand are ex ante uncertain. The sellers evaluate uncertain profits with maximin expected utilities exhibiting ambiguity aversion. The buyers in the market are permitted to split between sellers tieing at the minimum price in arbitrary ways which may be deterministic or random. The role (...) of the primitives in determining equilibrium prices in the market is analyzed in detail. (shrink)

We conducted a set of experiments to compare the effect of ambiguity in single-person decisions and games. Our results suggest that ambiguity has a bigger impact in games than in ball and urn problems. We find that ambiguity has the opposite effect in games of strategic substitutes and complements. This confirms a theoretical prediction made by Eichberger and Kelsey. In addition, we note that subjects’ ambiguity attitudes appear to be context dependent: ambiguity loving in single-person (...) decisions and ambiguity averse in games. This is consistent with the findings of Kelsey and le Roux. (shrink)

We survey the literature that has explored the implications of decision-making under ambiguity for financial market outcomes, such as portfolio choice and equilibrium asset prices. This ambiguity literature has led to a number of significant advances in our ability to rationalize empirical features of asset returns and portfolio decisions, such as the failure of the two-fund separation theorem in portfolio decisions, the modest exposure to risky securities observed for a majority of investors, the home equity preference in international (...) portfolio diversification, the excess volatility of asset returns, the equity premium and the risk-free rate puzzles, and the occurrence of trading break-downs. (shrink)

Incomplete information is a commonly cited barrier to the adoption of new innovations. We present a decision-making experiment, conducted with farmers in the field, that explores the extent to which information which reduces ambiguity may be provided as a public good. In the experiment, participants make a series of decisions between a risky gamble and an ambiguous gamble. An initial private decision is followed by second choice in which participants know that their chosen gambles and outcomes will be publicly (...) but anonymously revealed. Selection of the ambiguous option in this decision thus provide public good information which can be used to update beliefs about the ambiguous gamble. After the public revelation, participants make one final choice between the two options which we use to assess learning. We also test communication as a mechanism to increase provision of the public good. We find evidence that people with preference to avoid ambiguity contribute to public good information while risk averse people free ride. Communication does not affect the overall public good provision, either in a positive or negative direction. Finally, we find that people draw appropriate inference from the information that the public good provides. We relate our findings to the issue of new technology adoption in agriculture which is of particular importance for our participants. (shrink)

This article examines the effects of uncertainty aversion in competitive call option markets using a partial equilibrium model with the Choquet-expected utility setup. We find that the trading volume of a call option is negatively affected by uncertainty aversion, whereas the price of the call is practically independent of it.

The aim of this paper is to propose a preferences representation model where ambiguity attitudes can be exogenous events or past experience-dependent. We adapt the Recursive Smooth Ambiguity model proposed by Klibanoff (Journal of Economic Theory 144:930-976, 2009) by introducing past experience described by a sequence of neutral events occurring up to the moment of the decision. These neutral events do not provide any information on the true process, but are likely to strengthen or weaken the decision-maker’s (...) class='Hi'>ambiguity aversion degree by modifying emotions. Our model can explain some observed behaviors and market inefficiencies. We propose two illustrations. First, we provide a behavioral explanation for the decrease in influenza vaccination in France that followed the H1N1 crisis in 2009–2010. Second, we contribute to the broad literature on the annuity puzzle by introducing the impact of emotions on ambiguity attitudes. (shrink)

In this article, ambiguity attitude is measured through the maximum price a decision maker is willing to pay to know the probability of an event. Two problems are examined in which the decision maker faces an act: in one case, buying information implies playing a lottery, while, in the other case, buying information gives also the option to avoid playing the lottery. In both decision settings, relying on the Choquet expected utility model, we study how the decision maker’s risk (...) and ambiguity attitudes affect the reservation price for ambiguity resolution. These effects are analyzed for different levels of ambiguity of the act. Operating instructions for the elicitation of the reservation price for ambiguity resolution in an experimental setting are provided at the end of the article. (shrink)

The Ellsberg Paradox documented the aversion to ambiguity in the probability of winning a prize. Using an original sample of 266 business owners and managers facing risks from climate change, this paper documents the presence of departures from rationality in both directions. Both ambiguity-seeking behavior and ambiguity-averse behavior are evident. People exhibit ‘fear’ effects of ambiguity for small probabilities of suffering a loss and ‘hope’ effects for large probabilities. Estimates of the crossover point from (...) class='Hi'>ambiguity aversion (fear) to ambiguity seeking (hope) place this value between 0.3 and 0.7 for the risk per decade lotteries considered, with empirical estimates indicating a crossover mean risk of about 0.5. Attitudes toward the degree of ambiguity also reverse at the crossover point. (shrink)

Ambiguity affects decisions of people who exhibit a distaste of and require a premium for dealing with it. Do ambiguity-neutral subjects completely disregard ambiguity and react to any vague news? Online vending platforms often attempt to affect buyer’s decisions by messages like “20 people are looking at this item right now” or “The average score based on 567 reviews is 7.9/10”. We augment the two-color Ellsberg experiment with similarly worded signals about the unknown probability of success. All (...) decision-makers, including ambiguity-neutral, recognize and account for ambiguity; ambiguity-neutral subjects are less likely to respond to vague signals. The difference between decisions of ambiguity-neutral and non-neutral subjects vanishes for high precision signals; still less than 60% subjects choose the ambiguous urn, even for high communicated probabilities of success. We conjecture participants may discard information, if they see no contradiction between it and their prior beliefs, hence the latter are not updated. Higher confidence makes subjects more likely to discard the news, and empirically ambiguity-neutral subjects appear more confident than those ambiguity-averse. (shrink)

When preferences are such that there is no unique additive prior, the issue of which updating rule to use is of extreme importance. This paper presents an axiomatization of the rule which requires updating of all the priors by Bayes rule. The decision maker has conditional preferences over acts. It is assumed that preferences over acts conditional on event E happening, do not depend on lotteries received on Ec, obey axioms which lead to maxmin expected utility representation with multiple priors, (...) and have common induced preferences over lotteries. The paper shows that when all priors give positive probability to an event E, a certain coherence property between conditional and unconditional preferences is satisfied if and only if the set of subjective probability measures considered by the agent given E is obtained by updating all subjective prior probability measures using Bayes rule. (shrink)

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. (shrink)

Most decisions concerning insurance and self-protection have to be taken in situations in which the effort exerted precedes the moment uncertainty realizes, and the probabilities of future states of the world are not perfectly known. By integrating these two characteristics in a simple theoretical framework, this paper derives plausible conditions under which ambiguity aversion raises the demand for insurance and self-protection. In particular, it is shown that in most usual situations where the level of ambiguity does not (...) increase with the level of effort, a simple condition of ambiguity prudence known as decreasing absolute ambiguity aversion is sufficient to give a clear and positive answer to the question: Does ambiguity aversion raise the optimal level of effort? (shrink)

This paper reflects on the notion of partial ambiguity. Using a framework decomposing ambiguity into distinct layers of analysis, among which are risk and model uncertainty, and allowing for different attitudes toward these layers, I show that partial ambiguity may prove less desirable than full ambiguity, even under ambiguity aversion. This observation poses difficulties for interpreting the notion of partial ambiguity in relation to the partial information available to determine the potential compositions of (...) an ambiguous urn. Two Ellsberg-style thought experiments are described to challenge the meaning of partial ambiguity further, and an alternative interpretation, based on a more ambiguous relation, is discussed. (shrink)

We provide here a general mathematical framework to model attitudes towards ambiguity which uses the formalism of quantum theory as a “purely mathematical formalism, detached from any physical interpretation”. We show that the quantum-theoretic framework enables modelling of the Ellsberg paradox, but it also successfully applies to more concrete human decision-making tests involving financial, managerial and medical decisions. In particular, we elaborate a mathematical representation of various empirical studies which reveal that attitudes of managers towards uncertainty shift from (...) class='Hi'>ambiguity seeking to ambiguity aversion, and viceversa, thus exhibiting hope effects and fear effects. The present framework provides a promising direction towards the development of a unified theory of decisions in the presence of uncertainty. (shrink)

We report an experimental test of the influence of ambiguity on behaviour in a coordination game. We study the behaviour of subjects in the presence of ambiguity and attempt to determine whether they prefer to choose an ambiguity-safe option. We find that this strategy, which is not played in either Nash equilibrium or iterated dominance equilibrium, is indeed chosen quite frequently. This provides evidence that ambiguity-aversion influences behaviour in games. While the behaviour of the Row (...) Player is consistent with randomising between her strategies, the Column Player shows a marked preference for avoiding ambiguity and choosing his ambiguity-safe strategy. (shrink)

As illustrated by the famous Ellsberg paradox, many subjects prefer to bet on events with known rather than with unknown probabilities, i.e., they are ambiguity averse. In an experiment, we examine subjects’ choices when there is an additional source of ambiguity, namely, when they do not know how much money they can win. Using a standard assumption on the joint set of priors, we show that ambiguity-averse subjects should continue to strictly prefer the urn with known probabilities. (...) In contrast, our results show that many subjects no longer exhibit such a strict preference. (shrink)

This article addresses the value of information that affects the ambiguity faced by a decision maker. Our analysis is applied to the case of a farmer whose production can be damaged by a pest attack with unknown probability, this damage being reduced if the farmer decides to use a pesticide. Early warning systems have precisely been implemented in many countries to help farmers avoid inappropriate decisions in terms of pesticide use. We investigate, both theoretically and experimentally, how farmers value (...) these systems. We propose a two-state self-insurance model in which an α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-MaxMin Expected Utility farmer may use pesticides that reduce the loss in the accident state while incurring a cost in both states. Her decision to self-insure or not depends on risk and ambiguity attitudes. We compile and compare the value of two types of information leading to a reduction of ambiguity and analyze their properties with respect to ambiguity attitude. Both types of information are valued positively if the farmer is ambiguity averse. We conduct a framed field experiment in which farmers and agricultural students have to decide whether or not to apply pesticides depending on risk, ambiguity and the associated monetary gains resulting from pesticide cost. The experimental findings support the theory. The average value of information among all participants is between €0.9/ha and €3.3/ha depending on the information gain. (shrink)

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. (shrink)

This paper is about participation in efficient risk sharing among agents who have ambiguous beliefs about uncertain states of nature. The question we ask is whether and how can ambiguous beliefs give rise to some agents not participating in efficient risk sharing. Ambiguity of beliefs is described by the multiple-prior expected utility of Gilboa and Schmeidler, or the variational preferences of Maccheroni et al. :1447–1498, 2006). The main result says that if the aggregate risk is relatively small, then the (...) agents whose beliefs are the most ambiguous do not participate in risk sharing. The higher the ambiguity of those agents’ beliefs, the more likely is their non-participation. Another factor making non-participation more likely is low risk aversion of agents whose beliefs are less ambiguous. We discuss implications of our results on agents’ participation in trade in equilibrium in assets markets. (shrink)