Peter Klibanoff

Recursive smooth ambiguity preferences

This paper axiomatizes an intertemporal version of the Smooth Ambiguity decision model developed in Klibanoff, Marinacci, and Mukerji (2005). A key feature of the model is that it achieves a separation between ambiguity, identified as a characteristic of the decision makers subjective beliefs, and ambiguity attitude, a characteristic of the decision makers 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 accomodate 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.

Updating Preferences with Multiple Priors

We propose and axiomatically characterize dynamically consistent update rules for decision making under ambiguity. These rules apply to the preferences with multiple priors of Gilboa and Schmeidler (1989), and are the first, for any model of preferences over acts, to be able to reconcile typical behavior in the face of ambiguity (as exemplified by Ellsberg’s paradox) with dynamic consistency for all non-null events. Updating takes the form of applying Bayes’ rule to subsets of the set of priors, where the specific subset depends on the preferences, the conditioning event, and the choice problem (i.e., a feasible set of acts together with an act chosen from that set).

Maxmin Expected Utility over Savage Acts with a Set of Priors

When do dynamic nonconvexities at the disaggregate level translate into dynamic nonconvexities at the aggregate level? We address this question in a framework where the production of differentiated intermediate inputs is subject to dynamic nonconvexities and show that the answer depends on the degree of Hicks-Allen complementarity (substitutability) between differentiated inputs. In our simplest model, a generalization of Judd (1985) and Grossman and Helpman (1991) among many others, there are dynamic nonconvexities at the aggregate level if and only differentiated inputs are Hicks-Allen complements. We also compare dynamic equilibrium and optimal allocations in the presence of aggregate dynamic nonconvexities due to Hicks-Allen complementarities between differentiated inputs.

Decentralization, Externalities, and Efficiency

In the competitive model, externalities lead to inefficiencies, and inefficiencies increase with the size of externalities. However, as argued by Coase, these problems may be mitigated in a decentralized system through voluntary coordination. We show how coordination is limited by the combination of two factors: respect for individual autonomy and the existence of private information. Together they imply that efficient outcomes can only be achieved through coordination when external effects are relatively large. Moreover, there are instances in which coordination cannot yield any improvement at all, despite common knowledge that social gains from agreement exist. This occurs when external effects are relatively small, and this may help to explain why coordination is so seldom observed in practice. When improvements are possible, we describe how simple subsidies can be used to implement second-best solutions and explain why standard solutions, such as Pigovian taxes, cannot be used. Possible extensions to issues arising in the structure of research joint ventures, assumptions in the endogenous growth literature, and the location of environmental hazards are also described.

On the Smooth Ambiguity Model: A Reply

Epstein (2009) describes three Ellsberg-style thought experiments and argues that they pose difficulties for the smooth ambiguity model of decision making under uncertainty developed by Klibanoff, Marinacci and Mukerji (2005). We revisit these thought exeperiments and find, to the contrary, that they either point to strengths of the smooth ambiguity model compared to other models, such as the maximum expected utility model (Gilboa and Schmeidler, 1989), or, in the case of one thought experiment, raise criticisms that apply equally to a broad range of current ambiguity models.

Characterizing uncertainty aversion through preference for mixtures

Abstract. Uncertainty aversion is often modelled as (strict) quasi-concavity of preferences over uncertain acts. A theory of uncertainty aversion may be characterized by the pairs of acts for which strict preference for a mixture between them is permitted. This paper provides such a characterization for two leading representations of uncertainty averse preferences; those of Schmeidler [24] (Choquet expected utility or CEU) and of Gilboa and Schmeidler [16] (maxmin expected utility with a non-unique prior or MMEU). This characterization clarifies the relation between the two theories.

Stochastically independent randomization and uncertainty aversion

Summary. This paper proposes a preference-based condition for stochastic independence of a randomizing device in a product state space. This condition is applied to investigate some classes of preferences that allow for both independent randomization and uncertainty or ambiguity aversion (a la Ellsberg). For example, when imposed on Choquet Expected Utility (CEU) preferences in a Savage framework displaying uncertainty aversion in the spirit of Schmeidler [27], it results in a collapse to Expected Utility (EU). This shows that CEU preferences that are uncertainty averse in the sense of Schmeidler should not be used in settings where independent randomization is to be allowed. In contrast, Maxmin EU with multiple priors preferences continue to allow for a very wide variety of uncertainty averse preferences when stochastic independence is imposed. Additionally, these points are used to reexamine some recent arguments against preference for randomization with uncertainty averse preferences. In particular, these arguments are shown to rely on preferences that do not treat randomization as a stochastically independent event.

Experiments on Compound Risk in Relation to Simple Risk and to Ambiguity

We conduct experiments measuring individual behavior under compound risk, simple risk, and ambiguity. We focus on 1 treatment of compound risks relative to simple risks and 2 the relationship between compound risk attitudes and ambiguity attitudes. We find that compound risks are valued differently than corresponding reduced simple risks. These differences measure compound risk attitudes. These attitudes display more aversion as the reduced probability of the winning event increases. Like Halevy [Halevy Y 2007 Ellsberg revisited: An experimental study. Econometrica 75:503-536], we find an association between compound risk reduction and ambiguity neutrality. However, in contrast to the almost perfect identification in Halevys data, we find a substantially weaker relation in both directions. First, a majority of our ambiguity-neutral subjects fail to reduce compound risk. Second, almost a quarter of our subjects who reduce compound risk are nonneutral to ambiguity. All of the latter come from the more quantitatively sophisticated part of our subject pool. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2014.1953 . This paper was accepted by Peter Wakker, decision analysis.

Maxmin expected utility through statewise combinations

Abstract We provide an axiomatic foundation for a maxmin expected utility over a set of priors (MMEU) decision rule in an environment where the elements of choice are Savage acts. The key axioms are stated using statewise combinations as in Gul [Gul, F., 1992. Savage’s theorem with a finite number of states. Journal of Economic Theory 57, 99–100].

Perceived Ambiguity and Relevant Measures

We axiomatize preferences that can be represented by a monotonic aggregation of subjective expected utilities generated by a utility function and some set of i.i.d. probability measures over a product state space, S1. For such preferences, we define relevant measures, show that they are treated as if they were the only marginals possibly governing the state space and connect them with the measures appearing in the aforementioned representation. These results allow us to interpret relevant measures as reflecting part of perceived ambiguity, meaning subjective uncertainty about probabilities over states. Under mild conditions, we show that increases or decreases in ambiguity aversion cannot affect the relevant measures. This property, necessary for the conclusion that these measures reflect only perceived ambiguity, distinguishes the set of relevant measures from the leading alternative in the literature. We apply our findings to a number of well-known models of ambiguity-sensitive preferences. For each model, we identify the set of relevant measures and the implications of comparative ambiguity aversion.