Action-Independent Subjective Expected Utility without States of the World

Author(s)
Andreas Duus Pape

ABSTRACT

This paper develops an axiomatic theory of decision-making under uncertainty that has no state-space. The choice setting follows Karni [1,2]: a set of effects (outcomes), a set of actions which induce these effects, and a set of real-valued bets over effects. In Karni’s representation, a preference over action/bet pairs yields utility, which is action-dependent. In our representation, utility is action-independent. This is achieved by augmenting Karni’s choice set with lotteries over actions. Identification is achieved similarly to Anscombe-Aumann [3], in which there are objective “roulette” lotteries over subjective “horse race” lotteries.

This paper develops an axiomatic theory of decision-making under uncertainty that has no state-space. The choice setting follows Karni [1,2]: a set of effects (outcomes), a set of actions which induce these effects, and a set of real-valued bets over effects. In Karni’s representation, a preference over action/bet pairs yields utility, which is action-dependent. In our representation, utility is action-independent. This is achieved by augmenting Karni’s choice set with lotteries over actions. Identification is achieved similarly to Anscombe-Aumann [3], in which there are objective “roulette” lotteries over subjective “horse race” lotteries.

Cite this paper

A. Pape, "Action-Independent Subjective Expected Utility without States of the World,"*Theoretical Economics Letters*, Vol. 3 No. 5, 2013, pp. 17-21. doi: 10.4236/tel.2013.35A2004.

A. Pape, "Action-Independent Subjective Expected Utility without States of the World,"

References

[1] E. Karni, “Subjective Expected Utility Theory without States of the World,” Journal of Mathematical Economics, Vol. 42, No. 3, 2006, pp. 325-342. http://dx.doi.org/10.1016/j.jmateco.2005.08.007

[2] E. Karni, “A Theory of Bayesian Decision Making with Action-Dependent Subjective Probabilities,” Economic Theory, Vol. 48, No. 1, 2011, pp. 125-146.

[3] F. Anscombe and R. Aumann, “A Definition of Subjective Probability,” The Annals of Mathematical Statistics, Vol. 34, No. 1, 1963, pp. 199-205.

[4] I. Gilboa and D. Schmeidler, “Subjective Distributions,” Theory and Decision, Vol. 56, No. 4, 2004, pp. 345-357. http://dx.doi.org/10.1007/s11238-004-2596-7

[5] F. P. Ramsey, “The Foundations of Mathematics and Other Logical Essays: Truth and Probability,” Routledge and Kegan Paul, London, 1931, pp. 156-198.

[6] L. J. Savage, “The Foundations of Statistics,” Wiley, Hoboken, 1954.

[7] J. von Neumann and O. Morgenstern, “Theory of Games and Economic Behavior,” Princeton University Press, Princeton, 1944.

[8] D. M. Kreps, “Notes on the Theory of Choice. Underground Classics in Economics,” Westview Press, Inc., Fredrick A. Praeger, 1988.

[1] E. Karni, “Subjective Expected Utility Theory without States of the World,” Journal of Mathematical Economics, Vol. 42, No. 3, 2006, pp. 325-342. http://dx.doi.org/10.1016/j.jmateco.2005.08.007

[2] E. Karni, “A Theory of Bayesian Decision Making with Action-Dependent Subjective Probabilities,” Economic Theory, Vol. 48, No. 1, 2011, pp. 125-146.

[3] F. Anscombe and R. Aumann, “A Definition of Subjective Probability,” The Annals of Mathematical Statistics, Vol. 34, No. 1, 1963, pp. 199-205.

[4] I. Gilboa and D. Schmeidler, “Subjective Distributions,” Theory and Decision, Vol. 56, No. 4, 2004, pp. 345-357. http://dx.doi.org/10.1007/s11238-004-2596-7

[5] F. P. Ramsey, “The Foundations of Mathematics and Other Logical Essays: Truth and Probability,” Routledge and Kegan Paul, London, 1931, pp. 156-198.

[6] L. J. Savage, “The Foundations of Statistics,” Wiley, Hoboken, 1954.

[7] J. von Neumann and O. Morgenstern, “Theory of Games and Economic Behavior,” Princeton University Press, Princeton, 1944.

[8] D. M. Kreps, “Notes on the Theory of Choice. Underground Classics in Economics,” Westview Press, Inc., Fredrick A. Praeger, 1988.