Ben Polak

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.

Fictitious play in 2 x 2 games: a geometric proof of convergence*

SummaryThis paper provides a new proof of Miyasawas (1961) result showing the convergence of fictitious play in 2×2 games. The novelty of the approach used here is that it rests entirely on the geometric properties of the best-response correspondence. The geometric approach greatly shortens the exposition, and it suggests some possible extensions to more difficult convergence conjectures.

The Emergence of a National Capital Market in England, 1710–1880

Was eighteenth-century Londons financial market linked to domestic real capital markets? When did English capital markets cease to be regionally segmented? We compare London interest rates with annual registered property transactions in Middlesex and in West Yorkshire. This evidence, though tentative, suggests that London financial markets were weakly linked to local real capital markets in the mid-eighteenth century. By the late eighteenth century those links were strong. Regional markets were still segmented in the mid-eighteenth century but were integrated by the time of the Napoleonic War.

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.

Decomposable Choice under Uncertainty

Savage motivated his Sure Thing Principle by arguing that, whenever an act would be preferred if an event obtains and preferred if that event did not obtain, then it should be preferred overall. The idea that it should be possible to decompose and recompose decision problems in this way has normative appeal. We show, however, that it does not require the full separability across events implicit in Savages axiom. We formulate a weaker axiom that suffices for decomposability, and show that this implies an implicit additive representation. Our decomposability property makes local necessary conditions for optimality, globally sufficient. Thus, it is useful in computing optimal acts. It also enables Nash behavior in games of incomplete information to be decentralized to the agent-normal form. None of these results rely on probabilistic sophistication; indeed, our axiom is consistent with the Ellsberg paradox. If we assume probabilistic sophistication, however, then the axiom holds if and only if the agents induced preferences over lotteries satisfy betweenness.

Second-Order Expected Utility

We present two axiomatizations of the Second-Order Expected Utility model in the context of the standard models of choice under uncertainty.

Preference for information and dynamic consistency

We provide necessary and sufficient conditions for a dynamically consistent agent always to prefer more informative signals (in single-agent problems). These conditions do not imply recursivity, reduction or independence. We provide a simple definition of dynamically consistent behavior, and we discuss whether an intrinsic information lover (say, an anxious person) is likely to be dynamically consistent.