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| Expected utility theory | |
|---|---|
| Name | Expected utility theory |
| Introduced | 1940s |
| Protagonists | John von Neumann, Oskar Morgenstern, Frank P. Ramsey, Leonard J. Savage, John C. Harsanyi |
| Main concepts | Decision under risk, utility function, independence axiom, von Neumann–Morgenstern utility |
| Applications | Welfare economics, Financial economics, Game theory, Insurance |
Expected utility theory Expected utility theory provides a formal account of choice under risk by assigning numerical utilities to outcomes and prescribing choices that maximize the expected value of those utilities. It originated in mid-20th century mathematical work and has since shaped Game theory, Financial economics, Decision theory and policy analyses. The theory's axiomatic structure links preferences, risk attitudes, and optimization in contexts ranging from individual insurance decisions to strategic interaction among states and firms.
Expected utility theory was developed to explain how rational agents should choose among uncertain prospects by maximizing the expectation of a utility function over outcomes. The foundational formulation by John von Neumann and Oskar Morgenstern formalized utility in strategic contexts, while earlier contributions by Frank P. Ramsey and later formalizations by Leonard J. Savage expanded subjective probability treatments. The theory underpins normative models used in Welfare economics, Actuarial science, Portfolio theory, and models of bargaining in Game theory.
Axiomatic presentations specify preference relations on lotteries and derive representation theorems. The classic von Neumann–Morgenstern framework uses axioms such as completeness, transitivity, continuity, and the independence (or substitution) axiom to guarantee the existence of a cardinal utility function representing preferences over probabilistic mixtures. Alternative axiomatizations include Savage’s postulates, which replace objective probabilities with subjective probabilities derived from preferences and employ axioms like the Sure-Thing Principle. Influential contributors to axiomatic debates include John C. Harsanyi, Kenneth Arrow, and Milton Friedman in discussions connecting social choice and individual decision axioms.
Utility functions in expected utility theory are cardinal up to positive affine transformations: if u represents preferences, then au + b represents the same preference ordering for a > 0. Common parametric forms capture risk attitudes: the quadratic, exponential, and power utility families (including constant absolute risk aversion and constant relative risk aversion specifications) are widely used in applied Financial economics and Actuarial science. Von Neumann–Morgenstern utility interprets utilities as payoff transformations that make lotteries equivalent to their expected utilities; Savage’s framework yields subjective expected utility representations where beliefs correspond to probability measures determined by preference behavior. Important figures in functional representation include Lionel W. McKenzie and Leonard J. Savage.
The decision rule implied is straightforward: choose the act that maximizes expected utility. In Portfolio theory, this yields mean-variance optimization under specific utility forms; in insurance it explains demand for coverage under risk aversion. In strategic settings within Game theory, expected utility supports equilibrium concepts such as Nash equilibrium when players maximize expected payoff utilities. Public-policy and regulatory analysis by institutions like the World Bank and national agencies often use expected utility as a benchmark for cost–benefit calculations, while behavioral applications inform models of contract design in Labor economics and bidding strategies in Auction theory.
Several empirical and conceptual anomalies challenge the descriptive adequacy of expected utility. The Allais paradox and the Ellsberg paradox reveal violations of the independence axiom and ambiguity aversion, respectively, drawing attention from scholars such as Maurice Allais and Daniel Ellsberg. Other critiques focus on preference reversals, framing effects documented in experiments by Daniel Kahneman and Amos Tversky, and the difficulty of eliciting stable utilities in the presence of bounded rationality discussed by Herbert A. Simon. Theoretical objections include the problem of representing multiattribute outcomes and interpersonal comparisons of utility addressed in welfare debates involving Kenneth Arrow.
To address anomalies, several extensions generalize expected utility. Rank-dependent utility and cumulative prospect theory modify probability weighting to capture observed overweighting of small probabilities; key contributors include Paul Slovic and Daniel Kahneman alongside Amos Tversky. Models of ambiguity such as maxmin expected utility and multiple priors were developed by Daniel Ellsberg-inspired research and formalized by Gilboa and Schmeidler to represent ambiguity-averse preferences. Non-expected utility approaches, including prospect theory and regret theory, provide alternative representations that retain some axiomatic structure while relaxing independence or linear probability integration. Social-choice extensions examine expected utility aggregation and interpersonal utility comparisons in contexts explored by Kenneth Arrow and Amartya Sen.
Empirical tests compare observed choice behavior to predicted maximization of expected utility using laboratory experiments, field studies, and market data. Laboratory experiments by Vernon Smith and behavioral investigations by Daniel Kahneman and Amos Tversky produced systematic departures motivating richer descriptive models. Asset-pricing tests in Financial economics evaluate whether investor portfolios align with expected utility-maximizing behavior under rational expectations; empirical work by Eugene F. Fama and Robert J. Shiller examines anomalies such as excess volatility and return predictability. Experimental advances in neuroeconomics link decision patterns to neural correlates studied at institutions like National Institutes of Health, while large-scale field experiments test insurance purchase and savings behavior in development projects led by organizations such as the World Bank and International Monetary Fund.