Horst Zank

Parametric Weighting Functions

This paper provides preference foundations for parametric weighting functions under rank-dependent utility. This is achieved by decomposing the independence axiom of expected utility into separate meaningful properties. These conditions allow us to characterize rank-dependent utility with power and exponential weighting functions. Moreover, by allowing probabilistic risk attitudes to vary within the probability interval, a preference foundation for rank-dependent utility with parametric inverse-S shaped weighting function is obtained.

A Simple Preference-Foundation of Cumulative Prospect Theory with Power Utility

Most empirical studies of rank-dependent utility and cumulative prospect theory have assumed power utility functions, both for gains and for losses. As it turns out, a remarkably simple preference foundation is possible for such models: Tail independence (a weakening of comonotonic independence which underlies all rank-dependent models) together with constant proportional risk aversion suffice, in the presence of common assumptions (weak ordering, continuity, and first stochastic dominance), to imply these models. Thus, sign dependence, the different treatment of gains and losses, and the separation of decision weights and utility are obtained free of charge.

Axiomatizing the Harsanyi solution, the symmetric egalitarian solution and the consistent solution for NTU-games

Abstract.The validity of the axiomatization of the Harsanyi solution for NTU-games by Hart (1985) is shown to depend on the regularity conditions imposed on games. Following this observation, we propose two related axiomatic characterizations, one of the symmetric egalitarian solution (Kalai and Samet, 1985) and one of the consistent solution (Maschler and Owen, 1992). The three axiomatic results are studied, evaluated and compared in detail.

A new axiomatization of rank-dependent expected utility with tradeoff consistency for equally likely outcomes

Abstract This paper provides a new axiomatization of rank-dependent expected utility by relaxing tradeoff consistency to hold only when the involved outcomes are equally likely. The resulting weakened variant of tradeoff consistency is considerably simpler and intuitively more appealing than the original condition. Consequently, an improved tool for empirical studies and the elicitation of utilities is provided. It turns out that in the presence of weak ordering, simple-continuity, and stochastic dominance, the new tradeoff consistency for equally likely outcomes is sufficient to derive rank-dependent expected utility for general lotteries.

A Unified Derivation of Classical Subjective Expected Utility Models through Cardinal Utility

Classical foundations of expected utility were provided by Ramsey, de Finetti, von Neumann and Morgenstern, Anscombe and Aumann, and others. These foundations describe preference conditions to capture the empirical content of expected utility. The assumed preference conditions, however, vary among the models and a unifying idea is not readily transparent. Providing such a unifying idea is the purpose of this paper. The mentioned derivations have in common that a cardinal utility index for outcomes, independent of the states and probabilities, can be derived. Characterizing that feature provides the unifying idea of the mentioned models.

An Extension of Quasi-Hyperbolic Discounting to Continuous Time

Two-Stage Exponential (TSE) discounting, the model developed here, generalises exponential discounting in a parsimonious way. It can be seen as an extension of Quasi-Hyperbolic discounting to continuous time. A TSE discounter has a constant rate of time preference before and after some threshold time; the switch point. If the switch point is expressed in calendar time, TSE discounting captures time consistent behaviour. If it is expressed in waiting time, TSE discounting captures time invariant behaviour. We provide preference foundations for all cases, showing how the switch point is derived endogenously from behaviour. We apply each case to Rubinsteins infinite-horizon, alternating-offers bargaining model.

Rationality and Dynamic Consistency under Risk and Uncertainty

For choice with deterministic consequences, the standard rationality hypothesis is ordinality | i.e., maximization of a weak preference ordering. For choice under risk (resp. uncertainty), preferences are assumed to be represented by the objectively (resp. subjectively) expected value of a von Neumann{ Morgenstern utility function. For choice under risk, this implies a key independence axiom; under uncertainty, it implies some version of Savage’s sure thing principle. This chapter investigates the extent to which ordinality, independence, and the sure thing principle can be derived from more fundamental axioms concerning behaviour in decision trees. Following Cubitt (1996), these principles include dynamic consistency, separability, and reduction of sequential choice, which can be derived in turn from one consequentialist hypothesis applied to continuation subtrees as well as entire decision trees. Examples of behavior violating these principles are also reviewed, as are possible explanations of why such violations are often observed in experiments.