Expected utility theory from the frequentist perspective
Tóm tắt
We present an axiomatization of expected utility from the frequentist perspective. It starts with a preference relation on the set of infinite sequences with limit relative frequencies. We consider three axioms parallel to the ones for the von Neumann–Morgenstern (vN–M) expected utility theory. Limit relative frequencies correspond to probability values in lotteries in the vN–M theory. This correspondence is used to show that each of our axioms is equivalent to the corresponding vN–M axiom in the sense that the former is an exact translation of the latter. As a result, a representation theorem is established: The preference relation is represented by an average of utilities with weights given by the relative frequencies.
Tài liệu tham khảo
Anscombe F.J., Aumann R.: A definition of subjective probability. Ann Math Stat 34, 199–205 (1963)
Barbera S., Hammond P.J., Seidl C.: Handbook of Utility Theory: Principles, vol. 1. Kluwer, Dordrecht (1998)
Downey R., Hirschfeldt D., Nies A., Terwijn S.: Calibrating randomness. Bull Symb Logic 12, 411–491 (2006)
Fishburn P.C.: Utility Theory for Decision Making. Wiley, New York (1970)
Gillies D.: Philosophical Theories of Probability. Routlegde, London (2000)
Hu, T.-W.: Complexity and Mixed Strategy Equilibria. http://taiweihu.weebly.com/research.html (2009)
Kaneko M., Kline J.J.: Inductive game theory: a basic scenario. J Math Econ 44, 1332–1363 (2008)
Kaneko, M., Kline, J.J.: Transpersonal understanding through social roles, and emergence of cooperation. Tsukuba University, Department of Social Systems and Management Discussion Paper Series, No. 1228 (2009)
Martin-Löf P.: The definition of random sequences. Inform Control 9, 602–619 (1966)
Ville J.: Ĕtude Critique de la Concept du Collectif. Gauthier-Villars, Paris (1939)
von Mises R.: Probability, Statistics, and Truth, 2nd revised English edition. Dover, New York (1981)
von Neumann J., Morgenstern O.: Theory of Games and Economic Behavior. Princeton University, Princeton (1944)
Wald, A.: Die widerspruchsfreiheit des kollektivsbegriffes. In: Wald: Selected Papers in Statistics and Probability, pp. 25–41, 1955. New York: McGraw-Hill (1938)
Weatherford R.: Philosophical Foundations of Probability Theory. Routledge and Kegan Paul, London (1982)