Simon Grant

Choice under uncertainty with the best and worst in mind: Neo-additive capacities

We develop the simplest generalization of subjective expected utility that can accommodate both optimistic and pessimistic attitudes towards uncertainty-Choquet expected utility with non-extreme-outcome-additive (neo-additive) capacities. A neo-additive capacity can be expressed as the convex combination of a probability and a special capacity, we refer to as a Hurwicz capacity, that only distinguishes between whether an event is impossible, possible or certain. We show that neo-additive capacities can be readily applied in economic problems, and we provide an axiomatization in a framework of purely subjective uncertainty.

First Author Conditions

This paper provides a theoretical explanation for the persistent use of alphabetical name-orderings on academic papers in economics. In a context where market participants are interested in evaluating the relative individual contribution of authors, it is an equilibrium for papers to use alphabetical ordering. Moreover, it is never an equilibrium for authors always to be listed in order of relative contribution. In fact, we show via an example that the alphabetical name-ordering norm may be the unique equilibrium, although, multiple equilibria are also possible. Finally, we characterize the welfare properties of the noncooperative equilibrium and show it to produce research of lower quality than is optimal and than would be achieved if co-authors were forced to use name-ordering to signal relative contribution.

Temporal Resolution of Uncertainty and Recursive Non-Expected Utility Models ¤

If an agent (wealkly) prefers early resolution of uncertainty then the recursive forms of both the most commonly used non-expected utility models, betweenness and rank dependence, almost reduce to Kreps & Porteuss (1978) recurvise expected utility.

Generalized Utilitarianism and Harsanyi's Impartial Observer Theorem

We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyis impartial observer theorem. To do this, we reformulate Harsanyis problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (first) Diamonds critique concerning fairness and (second) Pattanaiks critique concerning differing attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyis utilitarianism.

The α-MEU model: A comment

In [7] Ghirardato, Macheroni and Marinacci (GMM) propose a method for distinguishing between perceived ambiguity and the decision-makers reaction to it. They study a general class of preferences which they refer to as invariant biseparable. This class includes CEU and MEU. They axiomatize a subclass of a-MEU preferences. If attention is restricted to finite state spaces, we show that any a-MEU preference relation, satisfies GMMs axioms if and only if a = 0 or 1, that is, the preferences must be either maxmin or maxmax. We show by example that these axioms may be satisfied when the state space is [0,1].

CEU preferences and dynamic consistency

This paper investigates the dynamic consistency of CEU preferences. A decision maker is faced with an information structure represented by a fixed filtration. If beliefs are represented by a convex capacity, we show that a necessary and sufficient condition for dynamic consistency is that beliefs be additive over the final stage in the filtration.

AUSI expected utility: An anticipated utility theory of relative disappointment aversion

In recent years there has been a growing theoretical, experimental and empirical challenge to Expected Utility Theory, the overwhelmingly dominant paradigm for modeling decision-making under risk. However, there has been relatively little work done in providing easily parameterized alternatives for applied work. In this paper we provide an axiomatization for a representation of preferences over lotteries that is only one parameter richer than expected utility. Our model is a special case of Quiggins Rank Dependent Expected Utility. Moreover, we show that the same restriction on this parameter is required for: risk aversion; intuitive comparative static results for a reasonably general class of economically interesting choice problems; and accommodating some of the most well-known violations of Expected Utility Theory.

Mean-Dispersion Preferences and Constant Absolute Uncertainty Aversion

We axiomatize, in an Anscombe-Aumann framework, the class of preferences that admit a representation of the form V(f) = mu - rho(d), where mu is the mean utility of the act f with respect to a given probability, d is the vector of state-by-state utility deviations from the mean, and rho(d) is a measure of (aversion to) dispersion that corresponds to an uncertainty premium. The key feature of these mean-dispersion preferences is that they exhibit constant absolute uncertainty aversion. This class includes many well-known models of preferences from the literature on ambiguity. We show what properties of the dispersion function rho(dot) correspond to known models, to probabilistic sophistication, and to some new notions of uncertainty aversion.

Many good choice Axioms: When can many-good lotteries be treated as money lotteries?

Abstract Without the Independence Axiom, a weaker substitution axiom, “ADI”, is necessary for the preferences over money lotteries induced by the money metric utility function to be well behaved. Given ADI, the agents preferences over many-good lotteries can be reconstructed from knowledge of preferences over money lotteries and over sure multivariate outcomes. Moreover, other substitution properties of underlying many-good lottery preferences are inherited by the money lottery preferences. We analyze the formal and intuitive nature of ADI and conclude that analysis of choice under uncertainty without ADI cannot be one dimensional.

Different notions of disappointment aversion

Abstract We discuss three notions of disappointment aversion, due to Gul [1991, Econometrica 59, 667-686], Grant and Kajii [1998, Journal of Economic Behavior and Organization 37, 277-290] and Skiadas [1997, Journal of Economic Theory 76, 242-271; 1997, Econometrica 65, 347-367], explaining how they differ. In the case of Gul and Skiadas we illustrate this difference by means of an example.