voprecotestВопросы экономикиVoprosy Ekonomiki0042-8736Voprosy Ekonomiki, NP10.32609/0042-8736-2009-10-46-61voprecotest-933Research ArticleВОПРОСЫ ТЕОРИИISSUES OF THEORYВероятность и неопределенность в экономическом моделированииProbability and Uncertainty in Economic ModelingГилбоаИ.GilboaI.

профессор

ПостлуэйтЭ.PostlewaiteW. A.

профессор экономики и финансов

 

ШмайдлерД.SchmeidlerD.

профессор

Университет Тель-Авива; Университет НЕС (Франция)ИзраильTel Aviv University; HEC Paris (France)IsraelУниверситет ПенсильванииСоединённые Штаты АмерикиUniversity of PennsylvaniaUnited StatesУниверситет Тель-Авива; Университет Огайо (США)ИзраильTel Aviv University; Ohio University (United States)Israel2009201020090104661Copyright © Voprosy Ekonomiki, NP, 20092009Voprosy Ekonomiki, NPVoprosy Ekonomiki, NPhttps://www.vopreco.ru/jour/about/submissions#copyrightNoticehttps://www.vopreco.ru/jour/article/view/933

В статье анализируются парадигма субъективной вероятности и теория ожидаемой полезности в их применении к теории принятия решений в условиях неопределенности. Показываются достоинства и недостатки аксиоматики Сэвиджа в теории субъективной вероятности, анализируются модели формирования верований. Предлагается новый подход к анализу принятия решений - модель множественных первичных верований, в которой агент приписывает каждому событию диапазон вероятностей.

The article considers the paradigm of subjective probability and expected utility theory with respect to their applications in the theory of decision-making. Advantages and shortcomings of Savage’s axiomatic in the subjective probability theory are analyzed, the models of beliefs formation are considered. The authors propose a new approach to the analysis of decision-making — a multiple priors model, where an agent attributes to each event not a single probability, but a range of probabilities.

теория субъективной вероятноститеория ожидаемой полезностимикроэкономическая теориятеория принятия решенийнеопределенностьsubjective probability theoryexpected utility theorymicroeconomicstheory of decision-makinguncertaintyReferencesAnscombe F. J., Aumann R. J. A Definition of Subjective Probability // Annals of Mathematical Statistics. 1963. Vol. 34, No 1. P. 199—205.Anscombe F. J., Aumann R. J. A Definition of Subjective Probability // Annals of Mathematical Statistics. 1963. Vol. 34, No 1. P. 199—205.Aragonès E., Gilboa I., Postlewaite A. W., Schmeidler D. Fact-Free Learning // American Economic Review. 2005. Vol. 95, No 5. P. 1355—1368.Aragonès E., Gilboa I., Postlewaite A. W., Schmeidler D. Fact-Free Learning // American Economic Review. 2005. Vol. 95, No 5. P. 1355—1368.Bewley T. Knightian Decision Theory: Part I // Decisions in Economics and Finance. 2002. Vol. 25, No 2. P. 79—110.Bewley T. Knightian Decision Theory: Part I // Decisions in Economics and Finance. 2002. Vol. 25, No 2. P. 79—110.Billot A., Gilboa I., Samet D., Schmeidler D. Probabilities as Similarity-Weighted Frequencies // Econometrica. 2005. Vol. 73, No 4. P. 1125—1136.Billot A., Gilboa I., Samet D., Schmeidler D. Probabilities as Similarity-Weighted Frequencies // Econometrica. 2005. Vol. 73, No 4. P. 1125—1136.Dow J., Werlang S. R. C. Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio // Econometrica. 1992. Vol. 60, No 1. P. 197—204.Dow J., Werlang S. R. C. Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio // Econometrica. 1992. Vol. 60, No 1. P. 197—204.Drèze J. Les fondements Logiques de l’Utilité cardinale et de la probabilité subjective // La Décision. P.: Colloques Internationaux du CNRS, 1961. P. 73—97.Drèze J. Les fondements Logiques de l’Utilité cardinale et de la probabilité subjective // La Décision. P.: Colloques Internationaux du CNRS, 1961. P. 73—97.Ellsberg D. Risk, Ambiguity and the Savage Axioms // Quarterly Journal of Economics. 1961. Vol. 75, No 4. P. 643—669.Ellsberg D. Risk, Ambiguity and the Savage Axioms // Quarterly Journal of Economics. 1961. Vol. 75, No 4. P. 643—669.Finetti B. de. La Prеvision: Ses Lois Logiques, Ses Sources Subjectives // Annales de l’Institute Henri Poincarе. 1937. Vol. 7, No 1. P. 1—68.Finetti B. de. La Prеvision: Ses Lois Logiques, Ses Sources Subjectives // Annales de l’Institute Henri Poincarе. 1937. Vol. 7, No 1. P. 1—68.Gilboa I., Lieberman O., Schmeidler D. Empirical Similarity // Review of Economics and Statistics. 2006. Vol. 88, No 3. P. 433—444.Gilboa I., Lieberman O., Schmeidler D. Empirical Similarity // Review of Economics and Statistics. 2006. Vol. 88, No 3. P. 433—444.Gilboa I., Postlewaite A. W., Schmeidler D. Rationality of Belief, or: Why Savage’s Axioms are neither Sufficient nor Necessary for Rationality // PIER Working Paper 07-001 / Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. 2006.Gilboa I., Postlewaite A. W., Schmeidler D. Rationality of Belief, or: Why Savage’s Axioms are neither Sufficient nor Necessary for Rationality // PIER Working Paper 07-001 / Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. 2006.Gilboa I., Schmeidler D. Maxmin Expected Utility with a Non-Unique Prior // Journal of Mathematical Economics. 1989. Vol. 18, No 2. P. 141—153.Gilboa I., Schmeidler D. Maxmin Expected Utility with a Non-Unique Prior // Journal of Mathematical Economics. 1989. Vol. 18, No 2. P. 141—153.Hacking I. The Emergence of Probability. Cambridge: Cambridge University Press, 1975.Hacking I. The Emergence of Probability. Cambridge: Cambridge University Press, 1975.Hansen L. P., Sargent T. J. Acknowledging Misspecification in Macroeconomic Theory // Review of Economic Dynamics. 2001. Vol. 4, No 3. P. 519—535.Hansen L. P., Sargent T. J. Acknowledging Misspecification in Macroeconomic Theory // Review of Economic Dynamics. 2001. Vol. 4, No 3. P. 519—535.Hansen L. P., Sargent T. J. Robust Control of Forward-Looking Models // Journal of Monetary Economics. 2003. Vol. 50, No 3. P. 581—604.Hansen L. P., Sargent T. J. Robust Control of Forward-Looking Models // Journal of Monetary Economics. 2003. Vol. 50, No 3. P. 581—604.Hansen L. P., Sargent T. J. Robustness. Princeton: Princeton University Press, 2007.Hansen L. P., Sargent T. J. Robustness. Princeton: Princeton University Press, 2007.Hansen L. P., Sargent T. J., Tallarini T. D. Robust Permanent Income and Pricing // Review of Economic Studies. 1999. Vol. 66, No 4. P. 873—907.Hansen L. P., Sargent T. J., Tallarini T. D. Robust Permanent Income and Pricing // Review of Economic Studies. 1999. Vol. 66, No 4. P. 873—907.Karni E. A. Definition of Subjective Probabilities with State-Dependent Preferences // Econometrica. 1993. Vol. 61, No 1. P. 187—198.Karni E. A. Definition of Subjective Probabilities with State-Dependent Preferences // Econometrica. 1993. Vol. 61, No 1. P. 187—198.Karni E. Elicitation of Subjective Probabilities when Preferences are State-Dependent // International Economic Review. 1999. Vol. 40, No 2. P. 479—486.Karni E. Elicitation of Subjective Probabilities when Preferences are State-Dependent // International Economic Review. 1999. Vol. 40, No 2. P. 479—486.Karni E. On the Representation of Beliefs by Probabilities // Journal of Risk and Uncertainty. 2003. Vol. 26, No 1. P. 17—38.Karni E. On the Representation of Beliefs by Probabilities // Journal of Risk and Uncertainty. 2003. Vol. 26, No 1. P. 17—38.Karni E. Probabilities and Beliefs // Journal of Risk and Uncertainty. 1996. Vol. 13, No 3. P. 249—262.Karni E. Probabilities and Beliefs // Journal of Risk and Uncertainty. 1996. Vol. 13, No 3. P. 249—262.Karni E., Schmeidler D., Vind K. On State Dependent Preferences and Subjective Probabilities // Econometrica. 1983. Vol. 51, No 4. P. 1021—1032.Karni E., Schmeidler D., Vind K. On State Dependent Preferences and Subjective Probabilities // Econometrica. 1983. Vol. 51, No 4. P. 1021—1032.Klibanoff P., Marinacci M., Mukerji S. A Smooth Model of Decision Making under Ambiguity // Econometrica. 2005. Vol. 73. No 6. P. 1849—1892.Klibanoff P., Marinacci M., Mukerji S. A Smooth Model of Decision Making under Ambiguity // Econometrica. 2005. Vol. 73. No 6. P. 1849—1892.Knight F. H. Risk, Uncertainty, and Profit. Boston, NY: Houghton Mifflin, 1921Knight F. H. Risk, Uncertainty, and Profit. Boston, NY: Houghton Mifflin, 1921Lichtenstein S., Slovic P. Reversals of Preferences between Bids and Choices Gambling Decisions // Journal of Experimental Psychology. 1971. Vol. 89, No 1. P. 46—55.Lichtenstein S., Slovic P. Reversals of Preferences between Bids and Choices Gambling Decisions // Journal of Experimental Psychology. 1971. Vol. 89, No 1. P. 46—55.Maccheroni F., Marinacci M., Rustichini A. Ambiguity Aversion, Robustness, and the Variational Representation of Preferences // Econometrica. 2006. Vol. 74, No 6. P. 1447—1498.Maccheroni F., Marinacci M., Rustichini A. Ambiguity Aversion, Robustness, and the Variational Representation of Preferences // Econometrica. 2006. Vol. 74, No 6. P. 1447—1498.Maccheroni F., Marinacci M., Rustichini A. Dynamic Variational Preference // Journal of Economic Theory. 2006. Vol. 128, No 1. P. 4—44.Maccheroni F., Marinacci M., Rustichini A. Dynamic Variational Preference // Journal of Economic Theory. 2006. Vol. 128, No 1. P. 4—44.Neumann J. von, Morgenstern O. Theory of Games and Economic Behavior. N. Y.: Wiley, 1944Neumann J. von, Morgenstern O. Theory of Games and Economic Behavior. N. Y.: Wiley, 1944Nishimura K., Ozaki H. Search and Knightian Uncertainty // Journal of Economic Theory. 2004. Vol. 119, No 2. P. 299—333.Nishimura K., Ozaki H. Search and Knightian Uncertainty // Journal of Economic Theory. 2004. Vol. 119, No 2. P. 299—333.Ramsey F. P. Truth and Probability // The Foundation of Mathematics and Other Logical Essays. N. Y.: Harcourt, Brace, 1931.Ramsey F. P. Truth and Probability // The Foundation of Mathematics and Other Logical Essays. N. Y.: Harcourt, Brace, 1931.Savage L. J. The Foundations of Statistics. N. Y.: John Wiley and Sons, 1954; 2nd ed. N. Y.: Dover, 1972.Savage L. J. The Foundations of Statistics. N. Y.: John Wiley and Sons, 1954; 2nd ed. N. Y.: Dover, 1972.Schmeidler D. Subjective Probability and Expected Utility without Additivity // Econometrica. 1989. Vol. 57, No 3. P. 571—587.Schmeidler D. Subjective Probability and Expected Utility without Additivity // Econometrica. 1989. Vol. 57, No 3. P. 571—587.Seo K. Ambiguity and Second-Order Belief. 2007. http://troi.cc.rochester.edu/_kseo/ambcom11052007.pdf.Seo K. Ambiguity and Second-Order Belief. 2007. http://troi.cc.rochester.edu/_kseo/ambcom11052007.pdf.Shafer G. Non-Additive Probabilities in the Work of Bernoulli and Lambert // Archive for History of Exact Sciences. 1978. Vol. 19, No 4. P. 309—370.Shafer G. Non-Additive Probabilities in the Work of Bernoulli and Lambert // Archive for History of Exact Sciences. 1978. Vol. 19, No 4. P. 309—370.Shafer G. Savage Revisited // Statistical Science. 1986. Vol. 1, No 4. P. 463—486.Shafer G. Savage Revisited // Statistical Science. 1986. Vol. 1, No 4. P. 463—486.Shea J. Childhood Deprivation and Adult Wealth. 2003. Unpublished paper.Shea J. Childhood Deprivation and Adult Wealth. 2003. Unpublished paper.Tversky A., Kahneman D. Judgment under Uncertainty: Heuristics and Biases // Science. 1974. Vol. 185, No 4157. P. 1124—1131.Tversky A., Kahneman D. Judgment under Uncertainty: Heuristics and Biases // Science. 1974. Vol. 185, No 4157. P. 1124—1131.

The authors declare that there are no conflicts of interest present.