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 principle of no-arbitrage, namely that neither an individual decision maker nor a small group of strategic competitors nor a large group of market participants should behave in such a way as to provide a riskless profit opportunity to an outside observer.Both those who work in the finance area and those who work in decision theory more broadly will be interested to find that basic tools from finance (arbitrage pricing and risk-neutral probabilities) have broader applications, including the modeling of subjective probability and expected utility, incomplete preferences, inseparable probabilities and utilities, nonexpected utility, ambiguity, noncooperative games, and social choice. Key results in all these areas can be derived from a single principle and essentially the same mathematics.A number of insights emerge from this approach. One is that the presence of money (or not) is hugely important for modeling decision behavior in quantitative terms and for dealing with issues of common knowledge of numerical parameters of a situation. Another is that beliefs (probabilities) do not need to be uniquely separated from tastes (utilities) for the modeling of phenomena such as aversion to uncertainty and ambiguity. Another over-arching issue is that probabilities and utilities are always to some extent indeterminate, but this does not create problems for the arbitrage-based theories.One of the book’s key contributions is to show how noncooperative game theory can be directly unified with Bayesian decision theory and financial market theory without introducing separate assumptions about strategic rationality. This leads to the conclusion that correlated equilibrium rather than Nash equilibrium is the fundamental solution concept.The book is written to be accessible to advanced undergraduates and graduate students, researchers in the field, and professionals.
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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.
1 Introduction1.1 Social physics1.2 The importance of having money1.3 The impossibility of measuring beliefs1.4 Risk-neutral probabilities1.5 No-arbitrage as common knowledge of rationality1.6 A road map of the book2 Preference axioms, fixed points, and separating hyperplanes2.1 The axiomatization of probability and utility2.2 The independence axiom2.3 The difficulty of measuring utility2.4 The fixed point theorem2.5 The separating hyperplane theorem2.6 Primal/dual linear programs to search for arbitrage opportunities2.7 No-arbitrage and the fundamental theorems of rational choice3 Subjective probability3.1 Elicitation of beliefs3.2 A 3-state example of probability assessment3.3 The fundamental theorem of subjective probability3.4 Bayes’ theorem and (not) learning over time3.5 Incomplete preferences and imprecise probabilities3.6 Continuous probability distributions3.7 Prelude to game theory: no-ex-post-arbitrage and zero probabilities4 Expected utility4.1 Elicitation of tastes4.2 The fundamental theorem of expected utility4.3 Continuous payoff distributions and measurement of risk aversion4.4 The fundamental theorem of utilitarianism (social aggregation)5 Subjective expected utility5.1 Joint elicitation of beliefs and tastes5.2 The fundamental theorem of subjective expected utility5.3 (In)separability of beliefs and tastes (state-dependent utility)5.4 Incomplete preferences with state-dependent utilities5.5 Representation by sets of probability/utility pairs6 State-preference theory, risk aversion, and risk-neutral probabilities6.1 The state-preference framework for choice under uncertainty6.2 Examples of utility functions for risk-averse agents6.3 The fundamental theorem of state-preference theory6.4 Risk-neutral probabilities and their matrix of derivatives6.5 The risk aversion matrix6.6 A generalized risk premium measure6.7 Risk-neutral probabilities and the Slutsky matrix7 Ambiguity and source-dependent risk aversion7.1 Introduction7.2 Ellsberg’s paradox and smooth non-expected-utility preferences7.3 Source-dependent utility revealed by risk-neutral probabilities7.4 A 3x3 example of a two-source model7.5 The second-order-uncertainty smooth model7.6 Discussion7.7 Some history of non-expected-utility8 Noncooperative games8.1 Introduction8.2 Solution of a 1-player game by no-arbitrage8.3 Solution of a 2-player game by no-arbitrage8.4 Games of coordination: chicken, battle of the sexes, and stag hunt8.5 An overview of correlated equilibrium and its properties8.6 The fundamental theorem of noncooperative games8.7 Examples of Nash and correlated equilibria8.8 Correlated equilibrium vsNash equilibrium and rationalizability8.9 Risk aversion and risk-neutral equilibria8.10 Playing a new game8.11 Games of incomplete information8.12 Discussion9 Asset pricing9.1 Introduction9.2 Risk-neutral probabilities and the fundamental theorem9.3 The multivariate normal/exponential/quadratic model9.4 Market aggregation of means and covariances9.5 The subjective capital asset pricing model (CAPM)10 Summary of the fundamental theorems and models10.1 Perspectives on the foundations of rational choice theory10.2 Axioms for preferences and acceptable bets10.3 Subjective probability theory10.4 Expected utility theory10.5 Subjective expected utility theory10.6 State-preference theory and risk-neutral probabilities10.7 Source-dependent utility and ambiguity aversion10.8 Noncooperative game theory10.9 Asset pricing theory11 Linear programming models for seeking arbitrage opportunities11.1 LP models for arbitrage in subjective probability theory11.2 LP model for for arbitrage in expected utility theory11.3 LP model for for arbitrage in subjective expected utility theory11.4 LP model for ex-post-arbitrage and correlated equilibria in games11.5 LP model for arbitrage in asset pricing theory12 Selected proofsBibliographyIndex
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Produktdetaljer

ISBN
9781032863511
Publisert
2025-01-31
Utgiver
Vendor
Chapman & Hall/CRC
Høyde
246 mm
Bredde
174 mm
Aldersnivå
U, P, 05, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
328

Forfatter

Biographical note

Robert Nau is a Professor Emeritus of Business Administration in the Fuqua School of Business, Duke University. He received his Ph.D. in Operations Research from the University of California at Berkeley. Professor Nau is an internationally known authority on mathematical models of decision-making under uncertainty. His research has been supported by the National Science Foundation, and his papers have been published in journals such as Operations Research, Management Science, Annals of Statistics, Journal of Economic Theory, and the International Journal of Game Theory. He was a co-recipient of the Decision Analysis Society Best Publication Award. One of the themes in Professor Nau’s research is that models of rational decision-making in various fields are linked by a single unifying principle, namely the principle of no-arbitrage, i.e., avoiding sure loss at the hands of a competitor. This principle is central to modern finance theory, but it can also be shown to be the fundamental rationality concept that underlies Bayesian statistics, decision analysis, and game theory. Professor Nau has taught the core MBA courses on Decision Models and Statistics in several programs, and he developed an MBA elective course on Forecasting, which he has taught throughout his career. He also teaches a course on Rational Choice Theory in the Ph.D. program that draws students from other departments and schools at Duke University.