Abstract
The standard model of decision analysis is modified by showing that, in general, the ‘state of nature’ concept can be usefully represented in terms of three components that may be called: (1) payoff relevant (2) payoff generating and (3) message generating. This modification allows a richer structure within which decision analysis problems can be formulated and thus allows a richer foundation for developing new concepts, classifying problems and revising existing concepts such as perfect information. It is shown that the unique payoff relevant domain of states and acts must, in any real decision, provide the initial basis for defining any payoff function (or, as appropriate, the loss function and opportunity loss function) that has a domain other than pay-off-relevant states.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Harold Bierman, Charles Bonini and Warren Hausman, Quantitative Analysis for Business Decisions, 3rd ed., Irwin, 1969.
Morris DeGroot, Optimal Statistical Decisions, McGraw-Hill, 1970.
Joel Demski, Information Analysis, Addison-Wesley, 1972.
Thomas Ferguson, Mathematical Statistics: A Decision Theoretical Approach, Academic Press, 1967.
Peter Fishburn, Utility Theory for Decision Making, John Wiley, 1970.
R. A. Howard, ‘The Foundations of Decision Analysis’, IEEE Transactions on Systems Science and Cybernetics, V. SSC4, No. 3, September, 1968.
Irving La Valle, An Introduction to Probability, Decision and Inference, Holt, Rinehart and Winston, 1972.
D. V. Lindley, Making Decisions, John Wiley, 1971.
R. D. Luce and H. Raiffa, Games and Decisions: Introduction and Critical Survey, John Wiley, 1957.
Jacob Marschak, ‘The Payoff-Relevant Description of States and Acts’, Econometrica, 31 (1963), 719.
C. B. McGuire and Roy Radner, Decision and Organization, North Holland, Amsterdam, 1972.
Howard Raiffa, Decision Analysis: Introductory Lectures on Choices Under Uncertainty, Addison-Wesley, 1968.
Howard Raiffa and Robert Schlaifer, Applied Statistical Decision Theory, Division of Research, Harvard Business School, 1961.
Leonard J. Savage, Foundations of Statistics, 2nd revised ed., Dover, 1972.
V. A. Rao Tummala, Decision Analysis with Business Applications, Intext, 1973.
John von Neumann and Oscar Morgenstern, Theory of Games and Economic Behavior, 2nd ed., Princeton, New Jersey, Princeton Press, 1947.
Robert L. Winkler, An Introduction to Bayesian Inference and Decision, Holt, Rinehart and Winston, 1972.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Berhold, M. Decision analysis model: An extension of the states of nature concept. Theor Decis 5, 275–288 (1974). https://doi.org/10.1007/BF00164719
Issue Date:
DOI: https://doi.org/10.1007/BF00164719