Showing papers on "Von Neumann–Morgenstern utility theorem published in 2001"

The economics of risk and time

Abstract: This book updates and advances the theory of expected utility as applied to risk analysis and financial decision making. Von Neumann and Morgenstern pioneered the use of expected utility theory in the 1940s, but most utility functions used in financial management are still relatively simplistic and assume a mean-variance world. Taking into account recent advances in the economics of risk and uncertainty, this book focuses on richer applications of expected utility in finance, macroeconomics, and environmental economics. The book covers these topics: expected utility theory and related concepts; the standard portfolio problem of choice under uncertainty involving two different assets; P the basic hyperplane separation theorem and log-supermodular functions as technical tools for solving various decision-making problems under uncertainty; s choice involving multiple risks; the Arrow-Debreu portfolio problem; consumption and saving; the equilibrium price of risk and time in an Arrow-Debreu economy; and dynamic models of decision making when a flow of information on future risks is expected over time. The book is appropriate for both students and professionals. Concepts are presented intuitively as well as formally, and the theory is balanced by empirical considerations. Each chapter concludes with a problem set.

Temptation and Self-Control

Abstract: We study a two-period model where ex ante inferior choice may tempt the decision-maker in the second period. Individuals have preferences over sets of alternatives that represent second period choices. Our axioms yield a representation that identifies the individual's commitment ranking, temptation ranking, and cost of self-control. An agent has a preference for commitment if she strictly prefers a subset of alternatives to the set itself. An agent has self-control if she resists temptation and chooses an option with higher ex ante utility. We introduce comparative measures of preference for commitment and self-control and relate them to our representations.

Psychological Expected Utility Theory and Anticipatory Feelings

Abstract: We extend expected utility theory to situations in which agents experience feelings of anticipation prior to the resolution of uncertainty. We show how these anticipatory feelings may result in time inconsistency. We provide an example from portfolio theory to illustrate the potential impact of anticipation on asset prices.

Making Descriptive Use of Prospect Theory to Improve the Prescriptive Use of Expected Utility

Abstract: This paper proposes a quantitative modification of standard utility elicitation procedures, such as the probability and certainty equivalence methods, to correct for commonly observed violations of expected utility. Traditionally, decision analysis assumes expected utility not only for the prescriptive purpose of calculating optimal decisions but also for the descriptive purpose of eliciting utilities. However, descriptive violations of expected utility bias utility elicitations. That such biases are effective became clear when systematic discrepancies were found between different utility elicitation methods that, under expected utility, should have yielded identical utilities. As it is not clear how to correct for these biases without further knowledge of their size or nature, most utility elicitations still calculate utilities by means of the expected utility formula. This paper speculates on the biases and their sizes by using the quantitative assessments of probability transformation and loss aversion suggested by prospect theory. It presents quantitative corrections for the probability and certainty equivalence methods. If interactive sessions to correct for biases are not possible, then the authors propose to use the corrected utilities rather than the uncorrected ones in prescriptions of optimal decisions. In an experiment, the discrepancies between the probability and certainty equivalence methods are removed by the authors' proposal.

Optimal payoff functions for members of collectives

Abstract: We consider the problem of designing (perhaps massively distributed) collectives of computational processes to maximize a provided "world utility" function. We consider this problem when the behavior of each process in the collective can be cast as striving to maximize its own payoff utility function. For such cases the central design issue is how to initialize/update those payoff utility functions of the individual processes so as to induce behavior of the entire collective having good values of the world utility. Traditional "team game" approaches to this problem simply assign to each process the world utility as its payoff utility function. In previous work we used the "Collective Intelligence" (COIN) framework to derive a better choice of payoff utility functions, one that results in world utility performance up to orders of magnitude superior to that ensuing from the use of the team game utility. In this paper, we extend these results using a novel mathematical framework. Under that new framework we review the derivation of the general class of payoff utility functions that both (i) are easy for the individual processes to try to maximize, and (ii) have the property that if good values of them are achieved, then we are assured a high value of world utility. These are the "Aristocrat Utility" and a new variant of the "Wonderful Life Utility" that was introduced in the previous COIN work. We demonstrate experimentally that using these new utility functions can result in significantly improved performance over that of previously investigated COIN payoff utilities, over and above those previous utilities' superiority to the conventional team game utility. These results also illustrate the substantial superiority of these payoff functions to perhaps the most natural version of the economics technique of "endogenizing externalities."

Why Would Nature Give Individuals Utility Functions

Abstract: Consider the possible biological origin of the expected utility criterion. On the one hand, if individuals possess a utility function stemming from the rate of production of expected offspring, they can rapidly adapt to arbitrary unknown distributions in a bandit problem. Embedding such a utility function in a simple rule of thumb involving no beliefs about probabilities leads to evolutionary optimality. On the other hand, if any rule whatever yields evolutionary optimality for all distributions, this precise utility function must be implicit, in a revealed preference sense.

Cumulative Prospect Theory for Parametric and Multiattribute Utilities

Abstract: Different attitudes towards gains and losses are a prominent feature of cumulative prospect theory for decision under uncertainty. In particular, decision weights for uncertain events can depend on whether the events involve gains or losses, and the shape of the utility function can reveal loss aversion. Decision analyses concentrate on event capacities, which determine decision weights, and on the shape of the utility function. The present paper focuses on linear/exponential, power-function and multilinear utility models for decision under uncertainty. We begin with straightforward preference axioms for a representation by a cumulative prospect theory functional. The axioms include weak ordering, continuity, monotonicity and tail independence. We show that in their presence constant absolute proportional risk aversion implies linear/exponential power utility. Then, for the multiattribute case, mutual utility independence leads to a utility function that is additive/multiplicative multilinear.

Non‐Expected Utility, Saving and Portfolios

Abstract: Despite increased stockholding opportunities, standard expected-utility models overpredict household participation and stock holdings. It has been suggested that departures from expected utility could resolve both puzzles. We investigate three measurable departures: (i) Kreps-Porteus preferences, (ii) Yaari's Dual Theory, and (iii) Quiggin's Rank-dependent Utility. Improvements tend to occur in predicted portfolio composition rather than participation. They are limited under (i), questionable under (ii), and more sizeable under (iii). Contrary to priors in the literature, improvements under (iii) do not result from solutions at kinks of indifference curves. We conclude that stockholding puzzles are unlikely to be resolved through preferences alone. Financial developments over the past decade have significantly enhanced the opportunities of households to invest in risky financial assets. Financial liberalisation led to considerable innovation, both in financial products and in the bundling of financial services. Privatisation of public utilities generated new stockholding opportunities, while the associated advertising campaign provided households with considerable information regarding the workings of the stock market. The proliferation of mutual funds allowed even small investors to hold highly diversified portfolios, and gave them access to the financial expertise of professional fund managers. Increased international integration and policy developments such as EMU improved prospects for risky asset holding across international borders. Pension reforms are encouraging households to undertake portfolio investments in order to provide for their old age. Progress in telecommunications and information channels, notably internet trading of securities and mutual funds, facilitate transactions. These important 'supply-side' developments have increased the number of stockholders, but have not been sufficient to induce the majority of house

A process approach to the utility for gambling

Abstract: This paper argues that any specific utility or disutility for gambling must be excluded from expected utility because such a theory is consequential while a pleasure or displeasure for gambling is a matter of process, not of consequences. A (dis)utility for gambling is modeled as a process utility which monotonically combines with expected utility restricted to consequences. This allows for a process (dis)utility for gambling to be revealed. As an illustration, the model shows how empirical observations in the Allais paradox can reveal a process disutility of gambling. A more general model of rational behavior combining processes and consequences is then proposed and discussed.

Probability Weighting in Choice under Risk: An Empirical Test

Abstract: This paper reports a violation of rank-dependent utility with inverse S-shaped probability weighting for binary gambles. The paper starts with a violation of expected utility theory: one-stage gambles elicit systematically different utilities than theoretically equivalent two-stage gambles. This systematic disparity does not disappear, but becomes more pronounced after correction for inverse S-shaped probability weighting. The data are also inconsistent with configural weight theory and Machina's fanning out hypothesis. Possible explanations for the data are loss aversion and anchoring and insufficient adjustment.

Parameters for Utilitarian Desires in a Qualitative Decision Theory

Abstract: In qualitative decision-theoretic planning, desires—qualitative abstractions of utility functions—are combined with defaults—qualitative abstractions of probability distributions—to calculate the expected utilities of actions. This paper is inspired from Lang's framework of qualitative decision theory, in which utility functions are constructed from desires. Unfortunately, there is no consensus about the desirable logical properties of desires, in contrast to the case for defaults. To do justice to the wide variety of desires we define parameterized desires in an extension of Lang's framework. We introduce three parameters, which help us to implement different facets of risk. The strength parameter encodes the importance of the desire, the lifting parameter encodes how to determine the utility of a set (proposition) from the utilities of its elements (worlds), and the polarity parameter encodes the relation between gain of utility for rewards and loss of utility for violations. The parameters influence how desires interact, and they thus increase the control on the construction process of utility functions from desires.

Strong One-Switch Utility

Abstract: The linear plus exponential utility function has received increasing attention of late as a particularly attractive family for evaluating additive gambles for wealth. In addition to its ability to reflect increasing appreciation for money, risk aversion, and decreasing risk aversion, it is consistent with a risk-return representation in which return is measured by expected value. In this paper we present a new condition, strong one-switch, that characterizes the linear plus exponential family.

Characterizing uncertainty aversion through preference for mixtures

Abstract: Uncertainty aversion is often modelled as (strict) quasi-concavity of preferences over uncertain acts. A theory of uncertainty aversion may be characterized by the pairs of acts for which strict preference for a mixture between them is permitted. This paper provides such a characterization for two leading representations of uncertainty averse preferences; those of Schmeidler [24] (Choquet expected utility or CEU) and of Gilboa and Schmeidler [16] (maxmin expected utility with a non-unique prior or MMEU). This characterization clarifies the relation between the two theories.

Uncertainty Aversion with Second-Order Probabilities and Utilities

Abstract: Aversion to uncertainty is commonly attributed to nonadditivity of subjective probabilities for ambiguous events, as in the Choquet expected utility model. This paper shows that uncertainty aversion can be parsimoniously explained by a simple model of “partially separable” non-expected utility preferences in which the decision maker satisfies the independence axiom selectively within partitions of the state space whose elements have similar degrees of uncertainty. As such, she may behave like an expected-utility maximizer with additive probabilities for assets in the same uncertainty class, while exhibiting higher degrees of risk aversion toward assets that are more uncertain. An alternative interpretation of the same model is that the decision maker may be uncertain about her credal state (represented by second-order probabilities for her first-order probabilities and utilities), and she may be averse to that uncertainty (represented by a secondorder utility function). The Ellsberg and Allais paradoxes are explained by way of illustration.

Calibration results for rank-dependent expected utility

Abstract: If its utility function is everywhere increasing and concave, rank-dependent expected utility shares a troubling property with expected utility -- aversion to the same moderate-stakes risk at every wealth level implies an extreme aversion to large-stakes risks. In fact, the problem may be even worse for rank-dependent expected utility, since the moderate-stakes risk need not be actuarially fair.

A Derivation of Expected Utility Maximization in the Context of a Game

Abstract: A decision maker faces a decision problem, or a game against nature. For each probability distribution over the state of the world (nature's strategies), she has a weak order over her acts (pure strategies). We formulate conditions on these weak orders guaranteeing that they can be jointly represented by expected utility maximization with respect to an almost-unique state-dependent utility, that is, a matrix assigning real numbers to act-state pairs. As opposed to a utility function that is derived in another context, the utility matrix derived in the game will incorporate all psychological or sociological determinants of well-being that result from the very fact that the outcomes are obtained in a given game.

On the Possibilistic-Based Decision Model: Characterization of Preference Relations Under Partial Inconsistency

Abstract: A qualitative counterpart to Von Neumann and Morgenstern's Expected Utility Theory of decision under uncertainty was recently proposed by Dubois and Prade. In this model, belief states are represented by normalised possibility distributions over an ordinal scale of plausibility, and the utility (or preference) of consequences of decisions are also measured in an ordinal scale. In this paper we extend the original Dubois and Prade's decision model to cope with partially inconsistent descriptions of belief states, represented by non-normalised possibility distributions. Subnormal possibility distributions frequently arise when adopting the possibilistic model for case-based decision problems. We consider two qualitative utility functions, formally similar to the original ones up to modifying factors coping with the inconsistency degree of belief states. We provide axiomatic characterizations of the preference orderings induced by these utility functions.

Lottery Dependent Utility: a Reexamination

Abstract: In order to accommodate empirically observed violations of the independence axiom of expected utility theory Becker and Sarin (1987) proposed their model of lottery dependent utility in which the utility of an outcome may depend on the lottery being evaluated. Although this dependence is intuitively very appealing and provides a simple functional form of the resulting decision criterion, lottery dependent utility has been nearly completely neglected in the recent literature on decision making under risk. The goal of this paper is to revive the lottery dependent utility model. Therefore, we derive first a sound axiomatic foundation of lottery dependent utility. Secondly, we develop a discontinuous variant of the model which can accommodate boundary effects and may lead to a lexicographic non-expected utility model. Both analyses are accompanied by considering some functional specifications which are in accordance with recent experimental results and may have significant applications in business and management science.

Rank dependent expected utility models of tax evasion

Abstract: In this paper the rank-dependent expected utility theory is substituted for the expected utility theory in models of tax evasion It is demonstrated that the comparative statics results of the expected utility, portfolio choice model of tax evasion carry over to the more general rank dependent expected utility model

The Firm Under Uncertainty with General Risk-Averse Preferences: A State-Contingent Approach

Abstract: This paper summarizes and synthesizes recent developments in the state-contingent theory of production under uncertainty presented by Chambers and Quiggin (2000) with a particular focus on the case of generalized expected utility preferences. The problem of the risk-averse firm under price and production uncertainty is analyzed using a state-contingent production technology and general risk-averse preferences. The concept of an efficient frontier, which identifies all potentially optimal production plans for weakly risk-averse decisionmakers, is introduced and used to develop comparative static results. For constant absolute risky technologies, the efficient frontier is shown to correspond to a unique isocost contour.

Range convexity and ambiguity averse preferences

Abstract: We show that range convexity of beliefs, a `technical' condition that appears naturally in axiomatizations of preferences in a Savage-like framework, imposes some unexpected restrictions when modelling ambiguity averse preferences. That is, when it is added to a mild condition, range convexity makes the preferences collapse to subjective expected utility as soon as they satisfy structural conditions that are typically used to characterize ambiguity aversion.

Non-Paternalistic Altruism and Utility Interdependence

Abstract: This paper clarifies the notion of non-paternalistic altruism through the use of utility aggregators. It presents conditions for the existence of non-paternalistically altruistic utility functions and provides a complete characterization of such utility functions. The results are used to generalize the Second Theorem of Welfare Economics and to prove the existence of an equilibrium in a game of voluntary gift-giving. JEL Classification Nos.: D11, D64.

On the existence and efficiency of the von Neumann-Morgenstern stable set in a n-player prisoners' dilemma

Abstract: We show that there exist von Neumann-Morgenstern (vN-M) stable sets in a n-player version of the prisoners' dilemma game with preplay negotiations in which every player can deviate unilaterally from the currently proposed combination of actions but can not do so jointly with other players, and that every vN-M stable set includes at least one Pareto-efficient outcome. The negotiation among the players is formulated as the “individual contingent threats situation” within the framework of the theory of social situations due to Greenberg (1990). The method of proving the existence also provides us with a step-by-step method of constructing the vN-M stable set.

Production under Uncertainty and Choice under Uncertainty in the Emergence of Generalized Expected Utility Theory

Abstract: This paper presents a personal view of the interaction between the analysis of choice under uncertainty and the analysis of production under uncertainty. Interest in the foundations of the theory of choice under uncertainty was stimulated by applications of expected utility theory such as the Sandmo model of production under uncertainty. This interest led to the development of generalized models including rank-dependent expected utility theory. In turn, the development of generalized expected utility models raised the question of whether such models could be used in the analysis of applied problems such as those involving production under uncertainty. Finally, the revival of the state-contingent approach led to the recognition of a fundamental duality between choice problems and production problems.

Decision and Choice: Paradoxes of Choice

Abstract: Paradoxes of choice are cases where people systematically violate descriptive theory. In the days of classical paradoxes, it was thought that a description of human choice would also be rational. Modern paradoxes are elegantly clear, systematic contradictions between human choices and descriptive theory, which may or may not be deemed rational. Choices that seem paradoxical from the viewpoint of old theories are explained by newer theory. The St Petersburg paradox, in which people prefer a small sum of money rather than play a gamble with infinite expected value, was explained in 1738 by Daniel Bernoulli, who theorized that utility of money is nonlinear. The paradoxes of Allais and Ellsberg showed that human choices do not conform to expected utility or subjective expected utility theory. Rank-dependent expected utility theory could describe the Allais and Ellsberg paradoxes. Birnbaum developed new paradoxes that refute rank-dependent expected utility theory as descriptive of human choice.

Compromises between Cardinality and Ordinality in Preference Theory and Social Choice

Abstract: By taking sets of utility functions as a primitive description of agents, we define an ordering over assumptions on utility functions that gauges their implicit measurement requirements. Cardinal and ordinal assumptions constitute two types of measurement requirements, but several standard assumptions in economics lie between these extremes. We first apply the ordering to different theories for why consumer preferences should be convex and show that diminishing marginal utility, which for complete preferences implies convexity, is an example of a compromise between cardinality and ordinality. In contrast, the Arrow-Koopmans theory of convexity, although proposed as an ordinal theory, relies on utility functions that lie in the cardinal measurement class. In a second application, we show that diminishing marginal utility, rather than the standard stronger assumption of cardinality, also justifies utilitarian recommendations on redistribution and axiomatizes the Pigou-Dalton principle. We also show that transitivity and order-density (but not completeness) characterize the ordinal preferences that can be induced from sets of utility functions, present a general cardinality theorem for additively separable preferences, and provide sufficient conditions for orderings of assumptions on utility functions to be acyclic and transitive.