Robert F. Nau

Book · January 1, 2025 This unique book offers a new approach to the modeling of rational decision-making under conditions of uncertainty and strategic and competition interactions among agents. It presents a unified theory in which the most basic axiom of rationality is the pri ... Full text Cite

Valuing risky projects: Option pricing theory and decision analysis

Chapter · November 1, 2017 In the academic literature and professional practice, there are a number of alternative and apparently competing methods for valuing risky projects. In this paper, we compare and contrast three different approaches: risk-adjusted discount-rate analysis, op ... Cite

Risk-neutral equilibria of noncooperative games

Journal Article Theory and Decision · February 1, 2015 Game-theoretic solution concepts such as Nash and Bayesian equilibrium start from an assumption that the players’ sets of possible payoffs, measured in units of von Neumann–Morgenstern utility, are common knowledge, and they go on to define rational behavi ... Full text Cite

Imprecise probabilities in non-cooperative games

Journal Article Isipta 2011 Proceedings of the 7th International Symposium on Imprecise Probability Theories and Applications · December 1, 2011 Game-theoretic solution concepts such as Nash equilibrium are commonly used to model strategic behavior in terms of precise probability distributions over outcomes. However, there are many potential sources of imprecision in beliefs about the outcome of a ... Cite

Risk, ambiguity, and state-preference theory

Journal Article Economic Theory · October 1, 2011 The state-preference framework for modeling choice under uncertainty, in which objects of choice are allocations of wealth or commodities across states of the world, is a natural one for modeling "smooth" ambiguity-averse preferences. It does not require r ... Full text Cite

A theorem for Bayesian group decisions

Journal Article Journal of Risk and Uncertainty · August 1, 2011 This paper presents a natural extension of Bayesian decision theory from the domain of individual decisions to the domain of group decisions. We assume that each group member accepts the assumptions of subjective expected utility theory with respect to the ... Full text Cite

Duality between maximization of expected utility and minimization of relative entropy when probabilities are imprecise

Conference Isipta 2009 Proceedings of the 6th International Symposium on Imprecise Probability Theories and Applications · December 1, 2009 In this paper we model the problem faced by a riskaverse decision maker with a precise subjective probability distribution who bets against a risk-neutral opponent or invests in a financial market where the beliefs of the opponent or the representative age ... Cite

Sensitivity to distance and baseline distributions in forecast evaluation

Journal Article Management Science · April 1, 2009 Scoring rules can provide incentives for truthful reporting of probabilities and evaluation measures for the probabilities after the events of interest are observed. Often the space of events is ordered and an evaluation relative to some baseline distribut ... Full text Cite

Scoring rules, generalized entropy, and utility maximization

Journal Article Operations Research · September 1, 2008 Information measures arise in many disciplines, including forecasting (where scoring rules are used to provide incentives for probability estimation), signal processing (where information gain is measured in physical units of relative entropy), decision an ... Full text Cite

Scoring rules, entropy, and imprecise probabilities

Journal Article Isipta 2007 Proceedings of the 5th International Symposium on Imprecise Probability Theories and Applications · December 1, 2007 Suppose that a risk-averse expected utility maximizer with a precise probability distribution p bets opti- mally against a risk neutral opponent (or equiva- lently invests in an incomplete market for contingent claims) whose beliefs (or prices) are describ ... Cite

Extensions of the Subjective Expected Utility Mode

Chapter · 2007 Cite

The shape of incomplete preferences

Journal Article Annals of Statistics · October 1, 2006 Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomple ... Full text Cite

Uncertainty aversion with second-order utilities and probabilities

Journal Article Management Science · January 1, 2006 Subjective expected utility theory does not distinguish between attitudes toward uncertainty (ambiguous probabilities) and attitudes toward risk (unambiguous probabilities). Both are explained in terms of nonlinear utility for money rather than properties ... Full text Cite

Bayesianism without priors, acts without consequences

Conference 4th International Symposium on Imprecise Probabilities and their Applications Isipta 2005 · January 1, 2005 A generalization of subjective expected utility is presented in which the primitives are a finite set of states of the world, a finite set of strategies available to the decision maker, and allocations of money. The model does not require explicit definiti ... Cite

On the geometry of Nash equilibria and correlated equilibria

Journal Article International Journal of Game Theory · January 1, 2004 It is well known that the set of correlated equilibrium distributions of an n-player noncooperative game is a convex polytope that includes all the Nash equilibrium distributions. We demonstrate an elementary yet surprising result: the Nash equilibria all ... Full text Cite

A generalization of Pratt-Arrow measure to nonexpected-utility preferences and inseparable probability and utility

Journal Article Management Science · January 1, 2003 The Pratt-Arrow measure of local risk aversion is generalized for the n-dimensional state-preference model of choice under uncertainty in which the decision maker may have inseparable subjective probabilities and utilities, unobservable stochastic prior we ... Full text Cite

The aggregation of imprecise probabilities

Journal Article Journal of Statistical Planning and Inference · June 15, 2002 Two methods are presented for the aggregation of imprecise probabilities elicited from a group of experts in terms of betting rates. In the first method, the experts bet with a common opponent subject to limits on their personal betting stakes, and their i ... Full text Cite

De Finetti was right: Probability does not exist

Journal Article Theory and Decision · December 1, 2001 De Finetti's treatise on the theory of probability begins with the provocative statement PROBABILITY DOES NOT EXIST, meaning that probability does not exist in an objective sense. Rather, probability exists only subjectively within the minds of individuals ... Full text Cite

Arbitrage, Incomplete Models, and Other People’s Brains

Chapter · 1999 Cite

Economic and Environmental Risk and Uncertainty New Models and Methods

Book · May 31, 1997 Audience: This work will be of interest to economists, management scientists, risk and policy analysts, and others who study risky decision-making in economic and environmental contexts. ... Cite

The incoherence of agreeing to disagree

Journal Article Theory and Decision · November 1, 1995 The agreeing-to-disagree theorem of Aumann and the no-expected-gain-from-trade theorem of Milgrom and Stokey are reformulated under an operational definition of Bayesian rationality. Common knowledge of beliefs and preferences is achieved through transacti ... Full text Cite

Valuing Risky Projects: Option Pricing Theory and Decision Analysis

Journal Article Management Science · May 1995 In the academic literature and professional practice, there are a number of alternative and apparently competing methods for valuing risky projects. In this paper, we compare and contrast three different approaches: risk-adjusted discount-rate ana ... Full text Cite

Coherent decision analysis with inseparable probabilities and utilities

Journal Article Journal of Risk and Uncertainty · January 1, 1995 This article explores the extent to which a decision maker's probabilities can be measured separately from his/her utilities by observing his/her acceptance of small monetary gambles. Only a partial separation is achieved: the acceptable gambles are partit ... Full text Cite

Indeterminate Probabilities on Finite Sets

Journal Article The Annals of Statistics · December 1, 1992 Full text Cite

Joint Coherence in Games of Incomplete Information

Journal Article Management Science · March 1992 Decisions are often made under conditions of uncertainty about the actions of supposedly-rational competitors. The modeling of optimal behavior under such conditions is the subject of noncooperative game theory, of which a cornerstone is Harsanyi' ... Full text Cite

Arbitrage, rationality, and equilibrium

Journal Article Theory and Decision · September 1, 1991 No-arbitrage is the fundamental principle of economic rationality which unifies normative decision theory, game theory, and market theory. In economic environments where money is available as a medium of measurement and exchange, no-arbitrage is synonymous ... Full text Cite

Coherent behavior in noncooperative games

Journal Article Journal of Economic Theory · January 1, 1990 A new concept of mutually expected rationality in noncooperative games is proposed: joint coherence. This is an extension of the "no arbitrage opportunities" axiom that underlies subjective probability theory and a variety of economic models. It sheds ligh ... Full text Cite

Decision analysis with indeterminate or incoherent probabilities

Journal Article Annals of Operations Research · December 1, 1989 This paper presents a new method of modeling indeterminate and incoherent probability judgments in decision analysis problems. The decision maker's degree of beliefs in the occurrence of an event is represented by a unimodal (in fact, concave) function on ... Full text Cite

Note—Blau's Dilemma Revisited

Journal Article Management Science · October 1987 The issue of equivalence between chance-constrained programming problems (CCPP's) and Bayesian utility-maximization problems (BUMP's), and the anomalous evaluation of information in CCPP's, are re-examined in light of a recent paper by Jagannathan ... Full text Cite

Should Scoring Rules be “Effective”?

Journal Article Management Science · May 1985 A scoring rule is a reward function for eliciting or evaluating forecasts expressed as discrete or continuous probability distributions. A rule is strictly proper if it encourages the forecaster to state his true subjective probabilities, and effe ... Full text Cite

Arma models for earthquake ground motions

Journal Article Earthquake Engineering Structural Dynamics · January 1, 1982 This paper outlines the use of discrete, autoregressive/moving‐average (ARMA) models for identification and estimation of parameters in models derived from analysis of uniformly digitized earthquake ground motion acceleration data. Such models are of equal ... Full text Cite

Simulating and analyzing artifical non-stationary earthquake ground motions.

Journal Article · December 1, 1980 This report describes models used to simulate earthquake accelerograms and analyses of these artifical accelerogram records for use in structural response studies. The artifical accelerogram records are generated by a class of linear difference equations w ... Cite

Adaptive filtering revisited

Journal Article Journal of the Operational Research Society · January 1, 1979 This paper shows that the adaptive filtering and forecasting techniques proposed by Makridakis and Wheelwright can be viewed as approximations to a more precise filtering method in which the Kalman filter is applied to a dynamic autoregressive model which ... Full text Cite