Risk, ambiguity, and the separation of utility and beliefs.

We introduce a general model of static choice under uncertainty, arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs. Most of the non-expected utility models existing in the literature are special cases of it. Such separation is motivated by the view that tastes are constant, whereas beliefs change with new information. The model has a simple and natural axiomatization. Elsewhere (forthcoming) we show that it can be very helpful in the characterization of a notion of ambiguity aversion, as separating utility and beliefs allows to identify and remove aspects of risk attitude from the decision maker’s behavior. Here we show that the model allows to generalize several results on the characterization of risk aversion in betting behavior. These generalizations are of independent interest, as they show that some traditional results for subjective expected utility preferences can be formulated only in terms of binary acts.

On Independence For Non-Additive Measures, With a Fubini Theorem

Recent models of decision making represent agents' beliefs by non-additive set-functions. An important technical question which arises in applications to diverse areas of economics is how to define independence of such set-functions. After arguing that the straightforward generalization of independence does not in general yield a unique product, in this work I show that, while Fubini's theorem is in general false if additivity is not granted, it is true when a certain type of function is being integrated. For these functions the iterated integrals coincide with the integral with respect to products which satisfy a certain property, strictly stronger than independence. I show that most of the assumptions made in these results are very close to being necessary. In general the mentioned property is still not strong enough to uniquely define a product. On the other hand I discuss some proposals which have been made in the literature, and I show that unicity can however be obtained when the product is assumed to be a belief function. Moreover I show that the unique product thus obtained has an intuitive justification when the marginals are distributions induced by random correspondences. Finally I use the results in the paper to discuss the question of randomization in decision models with non-additive beliefs

A more robust definition of multiple priors

This paper provides a multiple-priors representation of ambiguous beliefs à la Ghirardato, Maccheroni, and Marinacci (2004) and Nehring (2002) for any preference that is (i) monotonic, (ii) Bernoullian, i.e. admits an affine utility representation when restricted to constant acts, and (iii) suitably continuous. Monotonicity is the main substantive assumption: we do not require either Certainty Independence or Uncertainty Aversion. We characterize the set of ambiguous beliefs in terms of Clarke-Rockafellar differentials. This allows us to provide an explicit calculation of the set of priors for several recent decision models: multiplier preferences, the smooth ambiguity model, the vector expected utility model, as well as confidence function, variational, general "uncertainty-averse" preferences, and mean-dispersion preferences.Multiple Priors; Upper and Lower Probabilities; Ambiguity; Monotonic Preferences

Certainty Independence and the Separation of Utility and Beliefs.

Economists often operate under an implicit assumption that the tastes of a decision maker are constant, while his beliefs change with the availability of new information. It is therefore customary to seek representations of preferences which cleanly separate the taste component, called ‘utility,’ from the beliefs component. We show that a complete separation of utility from the other components of the representation is possible only if the decision maker’s preferences satisfy a mild but not completely innocuous condition, called ‘certainty independence.’ We prove that the preferences that obtain such separation are a subset of the biseparable preferences.nonatomic probability measures, we extend some of these results to the case of individuals with decreasing marginal evaluations.

Flexible Contracts

This paper studies the costs and benefits of delegating decisions to superiorly informed agents relative to the use of rigid, non discretionary contracts. Delegation grants some flexibility in the choice of the action by the agent, but also requires the use of an appropriate incentive contract so as to realign his interests with those of the principal. The parties’ understanding of the possible circumstances in which actions will have to be chosen and their attitude towards risk and uncertainty play then an important role in determining the costs of delegation. The main focus of the paper lies indeed in the analysis of these costs and the consequences for whether or not delegation is optimal. We determine and characterize the properties of the optimal flexible contract both when the parties have sharp probabilistic beliefs over the possible events in which the agent will have to act and when they only have a set of such beliefs. We show that the higher the agent’s degree of risk aversion, the higher the agency costs for delegation and hence the less profitable is a flexible contract versus a rigid one. The agent’s imprecision aversion in the case of multiple priors introduces another, additional agency costs; it again implies that the higher the degree of imprecision aversion the less profitable flexible contracts versus rigid ones. Even though, with multiple priors, the contract may be designed in such a way that principal and agent end up using ’different beliefs’ and hence engage in speculative trade, this is never optimal, in contrast with the case where the parties have sharp heterogeneous beliefs.Delegation, Flexibility, Agency Costs, Multiple Priors, Imprecision Aversion

Flexible Contracts

This paper studies the costs and benefits of delegating decisions to superiorly informed agents relative to the use of rigid, non discretionary contracts. Delegation grants some flexibility in the choice of the action by the agent, but also requires the use of an appropriate incentive contract so as to realign his interests with those of the principal. The parties’ understanding of the possible circumstances in which actions will have to be chosen and their attitude towards risk and uncertainty play then an important role in determining the costs of delegation. The main focus of the paper lies indeed in the analysis of these costs and the consequences for whether or not delegation is optimal.We determine and characterize the properties of the optimal flexible contract both when the parties have sharp probabilistic beliefs over the possible events in which the agent will have to act and when they only have a set of such beliefs. We show that the higher the agent’s degree of risk aversion, the higher the agency costs for delegation and hence the less profitable is a flexible contract versus a rigid one. The agent’s imprecision aversion in the case of multiple priors introduces another, additional agency costs; it again implies that the higher the degree of imprecision aversion the less profitable flexible contracts versus rigid ones. Even though, with multiple priors, the contract may be designed in such a way that principal and agent end up using ’different beliefs’ and hence engage in speculative trade, this is never optimal, in contrast with the case where the parties have sharp heterogeneous beliefs.delegation, flexibility, agency costs, multiple priors, imprecision aversion

Flexible contracts

This paper studies the costs and benefits of delegating decisions to superiorly informed agents relative to the use of rigid, non discretionary contracts. The main focus of the paper lies in the analysis of the costs of delegation, primarily agency costs, versus their benefits, primarily the flexibility of the action choice. We first determine and characterize the properties of the optimal flexible contract. We then show that the higher the agents's degree of risk aversion, the higher is the agency costs of delegation and the less profitable a flexible contract relative to a rigid one. When the parties to not have sharp probability beliefs, the agent's degree of imprecision aversion introduces another agency cost, which again reduces the relative profitability of flexible contracts.Delegation ; flexibility ; agency costs ; multiple priors ; imprecision aversion