Induced Preferences, Nonadditive Beliefs, and Multiple Priors

We study a decision maker who follows the Savage axioms. We show that if he or she is able to take unobservable actions that influence the probabilities of outcomes, then it can appear to an outsider as if his or her subjective probabilities are nonadditive. Implications for multiperiod decision are explored. We extend the model to include a second individual who is also able to take a hidden action. We show that this may induce uncertainty-averse preferences over some class of acts, even if the second individual acts to help the decision maker with high probability.     

Anchored preference relations

This note explores the implications of a simple and intuitive restriction on reference-dependent preferences assuming the status quo serves as the reference point. The condition imposed potentially rules out situations in which a decision maker has a choice between two prospects, selects one which subsequently becomes the new reference point, and then regrets her initial choice. It is shown that a surprising number of models in a riskless and risky setting violate this behavioral assumption, including Cumulative Prospect Theory as well as any theory exhibiting local non-satiation in which all reference-dependent indifference surfaces are smooth. It is also shown that the condition does admit a class of non-trivial reference-dependent preferences.     

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.     

State prices,liquidity, and default

We show, in a monetary exchange economy, that asset prices in a complete markets general equilibrium are a function of the supply of liquidity by the Central Bank, through its effect on default and interest rates. Two agents trade goods and nominal assets to smooth consumption across periods and future states, in the presence of cash-in-advance financing costs that have effects on real allocations. We show that higher spot interest rates reduce trade and as a result increase state prices. Hence, states of nature with higher interest rates are also states of nature with higher risk-neutral probabilities. This result, which cannot be found in a Lucas-type representative agent model, implies that the yield curve is upward sloping in equilibrium, even when short-term interest rates are fairly stable and the variance of the (macroeconomic) stochastic discount factor is 0. The risk-premium in the term structure is, therefore, a monetary-cost risk premium.     

Robustness and ambiguity in continuous time

We use statistical detection theory in a continuous-time environment to provide a new perspective on calibrating a concern about robustness or an aversion to ambiguity. A decision maker repeatedly confronts uncertainty about state transition dynamics and a prior distribution over unobserved states or parameters. Two continuous-time formulations are counterparts of two discrete-time recursive specifications of Hansen and Sargent (2007) [16]. One formulation shares features of the smooth ambiguity model of Klibanoff et al. (2005) and (2009) [24] and [25]. Here our statistical detection calculations guide how to adjust contributions to entropy coming from hidden states as we take a continuous-time limit.     

Subjective probability over a subjective decision tree

A state space has been assumed as a primitive for modeling uncertainty, which presumes that the analyst knows all the uncertainties a decision maker (DM) perceives. This is problematic because states are private information of the DM, and hence are not directly observable to the analyst. Dekel et al. [Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934] derive, rather than assume, the subjective state space from preference over suitable choice objects.In a dynamic setting, a decision tree, that is, a pair consisting of a state space and a filtration, has been taken as a primitive. This assumption is also problematic—a decision tree should be derived rather than assumed as a primitive. We formulate a three-stage extension of the above literature in order to model a DM who anticipates subjective uncertainty to be resolved gradually over time. We identify also subjective beliefs on the subjective state space.     

Differentiating ambiguity and ambiguity attitude

The objective of this paper is to show how ambiguity, and a decision maker (DM)'s response to it, can be modelled formally in the context of a general decision model. We introduce a relation derived from the DM's preferences, called “unambiguous preference”, and show that it can be represented by a set of probabilities. We provide such set with a simple differential characterization, and argue that it is a behavioral representation of the “ambiguity” that the DM may perceive. Given such revealed ambiguity, we provide a representation of ambiguity attitudes. We also characterize axiomatically a special case of our decision model, the “α-maxmin” expected utility model.     

Recursive smooth ambiguity preferences

This paper axiomatizes an intertemporal version of the Smooth Ambiguity decision model developed in [P. Klibanoff, M. Marinacci, S. Mukerji, A smooth model of decision making under ambiguity, Econometrica 73 (6) (2005) 1849-1892]. A key feature of the model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective beliefs, and ambiguity attitude, a characteristic of the decision maker's tastes. In applications one may thus specify/vary these two characteristics independent of each other, thereby facilitating richer comparative statics and modeling flexibility than possible under other models which accommodate ambiguity sensitive preferences. Another key feature is that the preferences are dynamically consistent and have a recursive representation. Therefore techniques of dynamic programming can be applied when using this model.     

Aggregation of multiple prior opinions

Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision maker?s utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Λ of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision maker?s set of priors is precisely all the weighted-averages of priors, where an expert?s prior is taken from her set and the weight vector is taken from Λ; (ii) the decision maker?s valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the experts? valuations.     

An extension of the multi-output state-contingent production model

This paper presents new developments on the state-contingent theory of production under uncertainty with stochastic prices. Our main purpose is to generalize the usual finite discrete state-contingent production model to infinite dimensional, possibly uncountable spaces which look like a more realistic framework. Usual duality results are established in this general context, shedding some light on the links between risk-neutral probabilities and shadow prices. A direct generalized production risk premium is defined and is shown to be independent of the inputs level when the technology is output translation homothetic. In such a case, the technology exhibits constant absolute riskiness. We thank Bob Chambers for his helpful comments.     

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].     

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.     

Proper scoring rules for general decision models

If a decision maker whose behavior conforms to the max-min expected utility model is faced with a scoring rule for a subjective expected utility decision maker, she will always announce a probability belonging to her set of priors; moreover, for any prior in the set, there is a scoring rule inducing the agent to announce that prior. We also show that on the domain of Choquet expected utility preferences with risk neutral lottery evaluation and totally monotone capacities, proper scoring rules do not exist. This implies the non-existence of proper scoring rules for any larger class of preferences (CEU with convex capacities, multiple priors).     

Coping with ignorance: unforeseen contingencies and non-additive uncertainty

Summary. In real-life decision problems, decision makers are never provided with the necessary background structure: the set of states of the world, the outcome space, the set of actions. They have to devise all these by themselves. I model the (static) choice problem of a decision maker (DM) who is aware that her perception of the decision problem is too coarse, as for instance when there might be unforeseen contingencies. I make a “bounded rationality' assumption on the way the DM deals with this difficulty, and then I show that imposing standard subjective expected utility axioms on her preferences only implies that they can be represented by a (generalized) expectation with respect to a non-additive measure, called a belief function. However, the axioms do have strong implications for how the DM copes with the type of ignorance described above. Finally, I show that some decision rules that have been studied in the literature can be obtained as a special case of the model presented here (though they have to be interpreted differently). Received: December 16, 1999; revised version: March 22, 2000     

Regret aversion and opportunity dependence

This paper provides an axiomatic model of decision making under uncertainty in which the decision maker is driven by anticipated ex post regrets. Our model allows both regret aversion and likelihood judgement over states to coexist. Also, we characterize two special cases, minimax regret with multiple priors that generalizes Savage's minimax regret, and a smooth model of regret aversion.     

Foundations of Bayesian theory

This paper states necessary and sufficient conditions for the existence, uniqueness, and updating according to Bayes’ rule, of subjective probabilities representing individuals’ beliefs. The approach is preference based, and the result is an axiomatic subjective expected utility model of Bayesian decision making under uncertainty with state-dependent preferences. The theory provides foundations for the existence of prior probabilities representing decision makers’ beliefs about the likely realization of events and for the updating of these probabilities according to Bayes’ rule.     

State-uncertainty preferences and the risk premium in the exchange rate market

This paper shows that state-uncertainty preferences help to explain the observed exchange rate risk premium. In the framework of Lucas (1982) economy, state-uncertainty preferences amount to assuming that a given level of consumption will yield a higher level of utility the lower is the level of uncertainty perceived by consumers. Under these preferences we can distinguish between two factors driving the exchange rate risk premium: “macroeconomic risk” and “the risk associated with variation in the private agents' perception on the level of uncertainty”. Empirical evidence from three main European economies in the transition period to the euro provides empirical support for the model. The model is more successful in accounting for the observed currency risk premium than models with more standard preferences, and the general perception of risk by private agents is shown to be a more important determinant of risk premium than macroeconomic uncertainty.     

USING ELICITED CHOICE PROBABILITIES TO ESTIMATE RANDOM UTILITY MODELS: PREFERENCES FOR ELECTRICITY RELIABILITY*

When choice data are not available, researchers studying preferences sometimes ask respondents to state the actions they would choose in choice scenarios. Data on stated choices are then used to estimate random utility models, as if they are data on actual choices. Stated and actual choices may differ because researchers typically provide respondents less information than they would have in actuality. Elicitation of choice probabilities overcomes this problem by permitting respondents to express uncertainty about behavior. This article shows how to use elicited choice probabilities to estimate random utility models and reports estimates of preferences for electricity reliability.     

Knightian Uncertainty in Financial Markets: An Assessment

If information is too vague and imprecise to be summarized by a unique additive probability measure, an agent faces Knightian uncertainty or ambiguity rather than risk. Under Knightian uncertainty, an agent's beliefs may be represented by a capacity or a set of additive probabilities. It is proved that an agent's attitude towards ambiguity has a crucial role in asset price determination and portfolio choice. Knightian uncertainty attitude provides an alternative explanation of financial market failures and enables puzzles to be solved, such as market breakdowns, price indeterminacy and volatility, bid and ask spreads, portfolio inertia, violation of call and put parity.
(J.E.L.: D81, G11, G12).     

Contracts payments for ecosystem services: the case of bio-pospecting

We examine the economics of royalties in bioprospecting contracts between a pharmaceutical and genetic resource supplier (local), with an eye to understanding the relative advantages of indexing royalty payments to gross revenue or net revenue. We show a risk-averse firm facing only production or only cost risks will index royalties to net revenue. When facing both types of risk, the choice of royalty type depends on the relative magnitudes of the production and cost risk. In each case, the risk-averse firm chooses the royalty type that shifts as much risk as possible to the local. When the local is risk neutral, the pharmaceutical's and local's preferences are compatible. If the local is risk averse and there is only one type of risk, it will prefer a gross revenue royalty, and shift as much risk as possible to the firm: here the local and firm preferences are compatible only if the firm is risk-neutral, Lastly, we show if the firm sets the terms of the contract, and both agents are risk averse, the firm will not likely volunteer to implement the socially optimal royalty arrangement as it prefers to shift as much risk to the local, who now also prefers a more certain return. This last outcome is at the heart of the benefit sharing discussion and suggests if risk sharing and equity are a concern in benefit sharing, then the choice of royalty type can be an important part of negotiations between pharmaceuticals and locals for the phytochemical from nature for new drug discovery.