A brain imaging study of the choice procedure

We study the behavior of subjects facing choices between certain, risky, and ambiguous lotteries. Subjects' choices are consistent with the economic theories modeling ambiguity aversion. Our results support the conjecture that subjects face choice tasks as an estimation of the value of the lotteries, and that the difficulty of the choice is an important explanatory variable (in addition to risk and ambiguity aversion).The brain imaging data suggest that such estimation is of an approximate nature when the choices involve ambiguous and risky lotteries, as the regions in the brain that are activated are typically located in parietal lobes. Thus such choices require mental faculties that are shared by all mammals, and in particular are independent of language. In contrast, choices involving partial ambiguous lotteries additionally produce an activation of the frontal region, which indicates a different, more sophisticated cognitive process.     

OPTIMISM AND PESSIMISM IN GAMES

This article considers the impact of ambiguity in strategic situations. It extends the existing literature on games with ambiguity‐averse players by allowing for optimistic responses to ambiguity. We use the CEU model of ambiguity with a class of capacities introduced by Jaffrray and Philippe (Mathematics of Operations Research 22 (1997), 165–85), which allows us to distinguish ambiguity from ambiguity‐attitude, and propose a new solution concept, equilibrium under ambiguity (EUA), for players who may be characterized by ambiguity‐preference. Applying EUA, we study comparative statics of changes in ambiguity‐attitude in games with strategic complements. This extends work in Eichberger and Kelsey (Journal of Economic Theory 106 (2002), 436–66) on the effects of increasing ambiguity if players are ambiguity averse.     

Ambiguity,data and preferences for information – A case-based approach

We model decision making under ambiguity based on available data. Decision makers express preferences over actions and data sets. We derive an α-max–min representation of preferences, in which beliefs combine objective characteristics of the data (number and frequency of observations) with subjective features of the decision maker (similarity of observations and perceived ambiguity). We identify the subjectively perceived ambiguity and separate it into ambiguity due to a limited number of observations and ambiguity due to data heterogeneity. The special case of no ambiguity provides a behavioral foundation for beliefs as similarity-weighted frequencies as in Billot et al. (2005) [3].     

Sealed bid auctions with ambiguity: Theory and experiments

This study presents a laboratory experiment of the first and second price sealed bid auctions with independent private values, where the distribution of bidder valuations may be unknown. In our experimental setting, in first price auctions, bids are lower with the presence of ambiguity. This result is consistent with ambiguity loving in a model that allows for different ambiguity attitudes. We also find that the first price auction generates significantly higher revenue than the second price auction with and without ambiguity.     

A behavioral characterization of plausible priors

Recent decision theories represent ambiguity via multiple priors, interpreted as alternative probabilistic models of the relevant uncertainty. This paper provides a robust behavioral foundation for this interpretation. A prior P is “plausible” if preferences over some subset of acts admit an expected utility representation with prior P, but not with any other prior Q≠P. Under suitable axioms, plausible priors can be elicited from preferences, and fully characterize them; also, probabilistic sophistication implies that there exists only one plausible prior; finally, “plausible posteriors” can be derived via Bayesian updating. Several familiar decision models are consistent with the proposed axioms.     

The effect of ambiguity aversion on reward scheme choice

We test the implications of ambiguity aversion in a principal–agent problem with multiple agents. Models of ambiguity aversion suggest that, under ambiguity, comparative compensation schemes may become more attractive than independent wage contracts. We test this by presenting agents with a choice between comparative reward schemes and independent contracts, which are designed such that under uncertainty about output distributions (that is, under ambiguity), ambiguity averse agents should typically prefer comparative reward schemes, independent of their degree of risk aversion. We indeed find that the share of agents who choose the comparative scheme is higher under ambiguity.     

Ambiguity aversion and trade

What is the effect of ambiguity aversion on trade? Although in a Bewley??s model, ambiguity aversion always leads to less trade; in other models, this is not always true. However, we show that if the endowments are unambiguous, then more ambiguity aversion implies less trade for a very general class of preferences. The reduction in trade caused by ambiguity aversion can be as severe as to lead to no trade. In an economy with MEU decision makers, we show that if the aggregate endowment is unanimously unambiguous, then every Pareto optima allocation is also unambiguous. We also characterize the situation in which every unanimously unambiguous allocation is Pareto optimal. Finally, we show how our results can be used to explain the home-bias effect. As a useful result for our methods, we also obtain an additivity theorem for CEU and MEU decision makers that does not require comonotonicity.     

Optimal greenhouse gas emissions under various assessments of climate change ambiguity

The probabilities associated with global warming damage are likely to be continuously revised in the light of new information. Such revisions of probability are the defining characteristic of ambiguity, as opposed to risk. This paper examines how climate change ambiguity may affect optimal greenhouse gas emission strategies, via the decision maker's attitude towards anticipated changes of damage probabilities. Two conceptualizations of ambiguity are distinguished, according to the emphasis placed on the ambiguity of priors or on the ambiguity of news, respectively. It is shown that the way in which ambiguity is viewed and the attitude taken towards it have a substantial influence on the optimal emission trajectory.     

Dragon Slaying with Ambiguity: Theory and Experiments

This paper studies the impact of ambiguity in the best‐shot and weakest‐link models of public good provision. The models are first analyzed theoretically. Then, we conduct experiments to study how ambiguity affects behavior in these games. We test whether subjects' perception of ambiguity differs between a local opponent and a foreign one. We find that an ambiguity‐safe strategy is often chosen by subjects. This is compatible with the hypothesis that ambiguity aversion influences behavior in games. Subjects tend to choose contributions above (respectively, below) the Nash equilibrium in the best‐shot (respectively, weakest‐link) model.     

Living with ambiguity: prices and survival when investors have heterogeneous preferences for ambiguity

This paper investigates asset prices and the long run wealth of investors in an asset market populated by investors who have heterogeneous preferences over risk and ambiguity. In a dynamic setting I characterize conditions under which investors who are averse to ambiguity will have an effect on long run asset prices. If ambiguity averse investors always believe that the true distribution could be wrong in many possible directions then a necessary condition for their survival is that the market exhibit no aggregate risk, a condition not met by many asset pricing models of interest. However, unlike investors with irrational beliefs, there do exist markets in which ambiguity averse investors survive. I have greatly benefitted from conversations with David Easley, Karl Shell, Ani Guerdjikova, Val Lambson, Kristian Rydqvist, Liyan Yang, Josh Teitelbaum and Jayant Ganguli as well as seminar participants at Cornell University and the Midwest Economic Theory Meetings. I am grateful to the Solomon Fund for Decision Research at Cornell University for support.     

Kindness,confusion, or … ambiguity?

Other-regarding preferences or decision errors are the main explanations put forward to justify contributions exceeding the non-cooperative optimum in VCM games. An alternative rationale relies on ambiguity aversion. Ambiguity aversion increases the perceived marginal benefit of own contributions, which in equilibrium will exceed the Nash level. We present a series of experiments testing this hypothesis. To control for other-regarding preferences, we run a two-player game in which a human player plays with a virtual agent. Players are assigned either to a risky setting (known probabilities of opponent’s choices) or to an ambiguity setting (probabilities of opponent’s contribution are vague). Results show that ambiguity affects contributions. However, attitude to ambiguity appears to be affected by the location of the aggregate Nash optimum inside the decision space.     

Ambiguity Without a State Space

Many decisions involve both imprecise probabilities and intractable states of the world. Objective expected utility assumes unambiguous probabilities; subjective expected utility assumes a completely specified state space. This paper analyses a third domain of preference: sets of consequential lotteries. Using this domain, we develop a theory of objective ambiguity without explicit reference to any state space. We characterize a representation that integrates a non-linear transformation of first-order expected utility with respect to a second-order measure. The concavity of the transformation and the weighting of the measure capture ambiguity aversion. We propose a definition for comparative ambiguity aversion.     

Ambiguity of scientific probability predictions and willingness-to-pay for climate change mitigation policies

We estimate a smooth ambiguity preference function, wherein an individual faces multiple probability predictions of policy outcomes, and then empirically measure their willingness-to-pay for the policy, ambiguity attitude, and ambiguity premium. Climate change mitigation policy is used as the example. The estimation results reveal that most people have ambiguity-seeking attitudes, but that these attitudes are heterogeneous across individuals. People who are older, are university graduates, have higher income, or trust more in science show stronger ambiguity-seeking attitudes. Their willingness-to-pay can be underestimated if ambiguity is not considered. Moreover, individuals with stronger ambiguity-seeking attitudes support aggressive mitigation policies more strongly. Our estimation strategy is generally applicable to policy evaluations wherein policy outcomes are ambiguous.     

Unintended hedging in ambiguity experiments

We describe an ambiguity hedging problem in Ellsberg experiments, where combinations of individually ambiguous bets eliminate aggregate ambiguity, and which may yield incorrect classifications of ambiguity averse subjects. We propose a new classification consistent with this hedging possibility.     

Modelling under ambiguity with dynamically consistent Choquet random walks and Choquet–Brownian motions

Ambiguity is pervasive in many environments and is increasingly being introduced into economic and financial models. This paper characterises ambiguity in the form of newly defined Choquet random walks: discrete-time binomial trees with capacities instead of exact probabilities on their branches. We describe the axiomatic basis of Choquet random walks, including dynamic consistency. We also discuss the convergence of Choquet random walks to Choquet–Brownian motion in continuous time. In contrast to previous literature, we derive tractable stochastic processes that allow for a wide range of ambiguity preferences to be represented in continuous time (including ambiguity-seeking preferences). Finally, we apply Choquet–Brownian ambiguity to a model of stationary inter-temporal portfolio choice. We find that both the mean and the variance of the underlying stochastic process are modified. This result opens the way for qualitative and quantitative results that differ from those of standard expected utility models and other models that feature ambiguity.     

A SMOOTH AMBIGUITY MODEL OF THE COMPETITIVE FIRM

This paper examines the optimal production decision of the competitive firm under price uncertainty when the firm's preferences exhibit smooth ambiguity aversion. Ambiguity is modeled by a second‐order probability distribution that captures the firm's uncertainty about which of the subjective beliefs govern the price risk. Ambiguity preferences are modeled by the (second‐order) expectation of a concave transformation of the (first‐order) expected utility of profit conditional on each plausible subjective distribution of the price risk. Within this framework, we derive necessary and sufficient conditions under which the ambiguity‐averse firm optimally produces less in response either to the introduction of ambiguity or to greater ambiguity aversion when ambiguity prevails. In the case that the price risk is binary, we show that ambiguity and greater ambiguity aversion always adversely affect the firm's production decision.     

Scientific Ambiguity and Climate Policy

Economic evaluation of climate policy traditionally treats uncertainty by appealing to expected utility theory. Yet our knowledge of the impacts of climate policy may not be of sufficient quality to be described by unique probabilistic beliefs. In such circumstances, it has been argued that the axioms of expected utility theory may not be the correct standard of rationality. By contrast, several axiomatic frameworks have recently been proposed that account for ambiguous knowledge. In this paper, we apply static and dynamic versions of a smooth ambiguity model to climate mitigation policy. We obtain a general result on the comparative statics of optimal abatement and ambiguity aversion, and then extend our analysis to a more realistic, dynamic setting, where we introduce scientific ambiguity into the well-known DICE model of the climate-economy system. For policy-relevant exogenous mitigation policies, we show that the value of emissions abatement increases as ambiguity aversion increases, and that this ‘ambiguity premium’ can in some plausible cases be very large. In these cases the effect of ambiguity aversion on welfare is comparable to that of other much studied welfare parameters. Thus ambiguity aversion may be an important neglected aspect of climate change economics, and seems likely to provide another argument for strong abatement policy.     

The dual theory of the smooth ambiguity model

This paper studies the “dual” theory of the smooth ambiguity model introduced by Klibanoff et al. (Econometrica 73:1849–1892, 2005). Unlike the original model, we characterize attitudes toward ambiguity captured by second-order probabilities. First, we give a set of axioms to derive a dual representation of the smooth ambiguity model. Second, we present a characterization of ambiguity aversion. Last, as an application of our dual model to a portfolio problem, we conduct comparative static predictions which give sufficient conditions to guarantee that an increase in smooth ambiguity aversion decreases the optimal portfolio.     

IMPACT OF OUTCOME AMBIGUITY ON SELF‐INSURANCE AND SELF‐PROTECTION: EXPERIMENTAL EVIDENCE

This experimental study examines and compares individual valuations of the two risk reduction mechanisms: self‐insurance and self‐protection in risky versus ambiguous outcome situations. Results confirm that individuals do not perceive these mechanisms differently under risk. Moreover, ambiguity in the outcome (i.e., size of loss) affects valuations weakly, and changing representations of ambiguity do not alter valuation. In general, individuals are found to be ambiguity averse for low sizes of loss and ambiguity neutral for high sizes of loss, regardless of the probability of loss. Finally, no strong support is found for any particular model of ambiguity.     

HEDGING AND THE COMPETITIVE FIRM UNDER AMBIGUOUS PRICE AND BACKGROUND RISK

This paper examines the optimal production and hedging decisions of the competitive firm that possesses smooth ambiguity preferences and faces ambiguous price and background risk. The separation theorem holds in that the firm's optimal output level depends neither on the firm's attitude towards ambiguity nor on the incident to the underlying ambiguity. We derive necessary and sufficient conditions under which the full‐hedging theorem holds and thus options are not used. When these conditions are violated, we show that the firm optimally uses options for hedging purposes if ambiguity is introduced to the price and background risk by means of mean‐preserving spreads. We as such show that options play a role as a hedging instrument over and above that of futures.