Search

Complexity of the problem of choosing among uncertain acts is a salient feature of many of the environments in which departures from expected utility theory are observed. I study a class of Generalized Simple Bounds preferences in which acts that are complex from the perspective of the decision maker are bracketed by "simple" acts to which they are related by statewise dominance. I then study a refinement of the model in which the size of the partition with respect to which an act is measurable arises endogenously as a measure of subjective complexity. Finally, I consider choice behavior characterized by a "cautious completion" of Simple Bounds preferences, and discuss the relationship between this model and models of ambiguity aversion. I develop general comparative statics results, and explore applications to portfolio choice and insurance choice. • Problems of choice problems under uncertainty are complex. • From behavioral axioms, I characterize the set of acts that are well-understood. • Decision makers use acts they understand well to bracket those they do not. • The model is tractable, and admits rich comparative statics. • The model helps explain observed choice patterns in applications. [ABSTRACT FROM AUTHOR]

This paper axiomatizes the representations of weighted utility theory with incomplete preferences. These include the general multiple weighted utility representation as well as special cases of multiple utilities or multiple weights only. Some behavioral implications are explored in the context of a portfolio selection problem, which illustrates the potential applicability of such models to a range of problems. • Representation of weighted utility theory with incomplete preferences. • Multi-weight multi-utility representation. • Multi-weight single utility and single weight multi-utility representation. [ABSTRACT FROM AUTHOR]

This paper substitutes the standard rationality assumption with approximate rationality in normal form games. We assume that players believe that their opponents might be ε -rational, i.e. willing to settle for a suboptimal choice, and so give up an amount ε of expected utility, in response to the belief they hold. For every player i and every opponents’ degree of rationality ε , we require player i to attach at least probability F i ( ε ) to his opponent being ε -rational, where the functions F i are assumed to be common knowledge amongst the players. We refer to this event as belief in F -rationality. The notion of Common Belief in F -Rationality ( CB F R ) is then introduced as an approximate rationality counterpart of the established Common Belief in Rationality. Finally, a corresponding recursive procedure is designed that characterizes those beliefs players can hold under CB F R . [ABSTRACT FROM AUTHOR]

Jensen’s inequality can be tightened in the context of discrete random variables. The suggested new inequality coincides with Jensen’s inequality only when the expected value of the random variable is an integer, in all other cases the inequality is tighter than Jensen’s. This improvement is used to derive a welfare result in the context of a mating market where male agents are exposed to paternal uncertainty. It is shown that social welfare is highest when paternity is certain, a result that cannot be obtained when relying on Jensen’s inequality. [ABSTRACT FROM AUTHOR]

We consider a model with an infinite number of states of nature, von Neumann–Morgenstern utilities, where agents have different probability beliefs and where short sells are allowed. We show that no-arbitrage conditions, defined for finite dimensional asset markets models, are not sufficient to ensure existence of equilibrium in presence of an infinite number of states of nature. However, if the individually rational utility set U is compact, we obtain an equilibrium. We give conditions which imply the compactness of U . We give examples of non-existence of equilibrium when these conditions do not hold. [ABSTRACT FROM AUTHOR]

We focus on the situation in which agents might have mutually singular beliefs in a maxmin expected utility framework. We show the existence of an equilibrium under fairly general conditions. We further demonstrate that the characterization of Pareto optimal allocation is significantly different from the classical situation, where all beliefs are mutually equivalent for each agent. Absent aggregate uncertainty, we prove that with common beliefs among agents, any Pareto optimal allocation is a full insurance under the upper capacities for all agents. But the full insurance feature of all Pareto optimal allocations, if true, does not necessarily ensure common beliefs. Moreover, despite agents have sharing beliefs, a full insurance Pareto optimal allocation could be associated with intricate allocation form. [ABSTRACT FROM AUTHOR]

Abstract: In a seminal paper, Becker (1968) showed that the most efficient way to deter crime is to impose the severest possible penalty (to maintain adequate deterrence) with the lowest possible probability (to economize on costs of enforcement). We shall call this the Becker proposition (BP). The BP is derived under the assumptions of expected utility theory (EU). However, EU is heavily rejected by the evidence. A range of non-expected utility theories have been proposed to explain the evidence. The two leading alternatives to EU are rank dependent utility (RDU) and cumulative prospect theory (CP). The main contributions of this paper are: (1) we formalize the BP in a more satisfactory manner; (2) we show that the BP holds under RDU and CP; and (3) we give a formal behavioral approach to crime and punishment that could have applicability to a wide range of problems in the economics of crime. [Copyright &y& Elsevier]

Abstract: This paper axiomatizes expected multi-utility representations of incomplete preferences under risk and under uncertainty. The von Neumann–Morgenstern expected utility model with incomplete preferences is revisited using a “constructive” approach, as opposed to earlier treatments that use convex analysis. [Copyright &y& Elsevier]

Abstract: We consider a decision maker facing uncertainty which behaves as a subjective expected utility maximizer. The value of information is traditionally captured as a greater expected utility the decision maker can achieve by selecting a best strategy as information arrives. We deal with the limit process of being better informed, and introduce an information density function depending solely on the states that gives an exact least upper bound to being more informed. This information density function is given by a Radon–Nikodym-type theorem for set functions and is explicitly computed for the countable case. [Copyright &y& Elsevier]

Abstract: This paper shows that the notions of prudence, temperance, edginess, and, more generally, risk apportionment of any degree are the consequences of the natural idea that the sensitivity to detrimental changes should decrease with initial wealth. In the setting of , this turns out to be equivalent to the supermodularity of the expected utility for some specific 4-state lotteries. [ABSTRACT FROM AUTHOR]

Abstract: An expert, trying to assess the true distribution over the states of nature, is associated with a preference relation over utility bundles. He prefers to if he believes that, according to the true distribution, the expected utility of is greater than that of . Expert is said to be more knowledgeable than expert () if, between the two experts, it is always beneficial to follow his advice. It is shown that if experts’ maxmin preferences are induced by information consistent with the true distribution, then in most cases an expert having more information is not more knowledgeable. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is two-fold: first, to emphasize that the seminal result of remains valid under weaker conditions, and this even if non-positive prices are considered, or equally that the no-trade interval result is robust when considering assets which can yield non-positive outcomes. Second, to make precise the weak uncertainty aversion behavior characteristic of the existence of such an interval. [Copyright &y& Elsevier]

Abstract: We identify conditions under which receipt of information in the form of a (potentially) ambiguous signal leads to a smoother maximin expected utility (MEU) preference structure which translates behaviorally into a smaller no-trade price zone. Narrowing of the no-trade price zone depends critically on the rectangularity of the belief structure, which, in the context of an MEU model, is a requirement of dynamic consistency in Machina’s sense. Another important factor affecting the size of the no-trade price zone is the relative contribution of ambiguity in signals and ambiguity in posterior beliefs to the degree of prior ambiguity over market events. [Copyright &y& Elsevier]

Abstract: An axiomatic account of rational risky choice is given which makes the impact of the decision maker''s economic situation on his preferences explicit. The constraints on rationality include the decision maker''s aspirations, uncertainties of current wealth and income (status quo), and the dependence of risk attitudes on background risks. Preferences admit a unique explicit utility representation in a suitable normalisation of the utility scale. The utility functional is generally non-linear in the probabilities and non-separable, but otherwise mathematically simple. It explicates well-known empirical features of utility-oriented behaviour such as the Allais paradox, observed variations in risk attitude and systematic violations of betweenness. [Copyright &y& Elsevier]

Abstract: An income distribution is a mixture of two given income distributions if the relative frequency it associates with each income level is a convex combination of the relative frequencies associated with it by the given two income distributions—e.g., the income distribution of a country is obtained as a mixture of the income distributions of its regions. In this article, it is established that all inequality measures commonly considered in the literature—the class of decomposable inequality measures and the class of normative inequality measures based on a social welfare function of the rank-dependent expected utility form—satisfy quasi-concavity properties, which imply, loosely speaking, that mixing income distributions increases inequality. These quasi-concavity properties are then shown to greatly reduce the possible patterns describing the evolution of inequality in the overall income distribution (a mixture) during a process in which population gradually shifts from one of its constituent income distributions to another over time. [Copyright &y& Elsevier]

In a previous paper [Cahiers de la M.S.E. (1999) 86] we proved that for RDEU (rank-dependent expected utility) maximizing MM (market-makers) with non-increasing marginal utility, positivity of the bid–ask spread can be identified with a very weak form of risk aversion SMRA (symmetrical monotone risk aversion). We perform here a more thorough study of SMRA, firstly in a general setting, and secondly in connection with the general RDEU model. Concerning the first point, SMRA is shown to be characterized via simple symmetric monotone spreads. As for the second issue, we characterize SMRA for the general RDEU model through a comparison of an index of pessimism (linked to the probability transformation function f) with an index of greediness (linked to the utility function u) in a similar way as done earlier for monotone risk aversion [Cahiers d’Ecomath (1997) 53]. [Copyright &y& Elsevier]