Abstract
People are less willing to accept bets about an event when they do not know the true probability of that event. Such “uncertainty aversion” has been used to explain certain economic phenomena. This paper considers how far standard private information explanations (with strategic decisions to accept bets) can go in explaining phenomena attributed to uncertainty aversion. This paper shows that if two individuals have different prior beliefs about some event, and two sided private information, then each individual’s willingness to bet will exhibit a bid ask spread property. Each individual is prepared to bet for the event, at sufficiently favorable odds, and against, at sufficiently favorable odds, but there is an intermediate range of odds where each individual is not prepared to bet either way. This is only true if signals are distributed continuously and sufficiently smoothly. It is not true, for example, in a finite signal model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Bewley, T.: 1986, ‘Knightian Decision Theory: Part I’, Cowles Foundation Discussion Paper No. 807.
Bewley, T.: 1987, ‘Knightian Decision Theory: Part II’, Cowles Foundation Discussion Paper No. 835.
Bewley, T.: 1988, ‘Knightian Decision Theory and Econometric Inference’, Cowles Foundation Discussion Paper No. 868.
Bewley, T.: 1989, ‘Market Innovation and Entrepreneurship: A Knightian View’, Cowles Foundation Discussion Paper No. 905.
Blackwell, D.: 1951, ‘The Comparison of Experiments’, in Proceedings, Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 93-102, University of California Press.
Borel, E.: 1924, ‘Apropos of a Treatise on Probability’, Revue Philosophique, translated and reprinted Studies in Subjective Probability, Kyburg and Smokler eds. (1st edition). John Wiley and Sons (1964).
Bulow, J., Geanakoplos, J. and Klemperer, P.: 1985, ‘Multimarket Oligopoly: Strategic Substitutes and Complements’, Journal of Political Economy 93, 488-511.
de Finetti, B.: 1937, ‘La Prevision: Ses Lois Logiques, Ses Sources Subjectives’, Annales de l’InstitutHenri Poincaré 7, 1-68, translated in English as ‘Foresight: its logical laws, its subjective sources’ and reprinted in Kyburg and Smokler (1980), pp. 53-118.
Dempster, A.: 1967, ‘Upper and Lower Probabilities Induced by a Multivalued Mapping’, Annals of Mathematical Statistics 38, 325-339.
Dempster, A.: 1968, ‘A Generalization of Bayesian Inference’, Journal of the Royal Statistical Society, Series B 30, 205-247.
Dow, J. and Werlang, S.: 1992, ‘Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio’, Econometrica 60, 197-204.
Dow, J., and Werlang, S.: 1994, ‘Nash Equilibrium Under Knightian Uncertainty: Breaking Down Backward Induction’, Journal of Economic Theory 64, 305-324.
Ellsberg, D.: 1961, ‘Risk, Ambiguity and the Savage Axioms’, Quarterly Journal of Economics 75, 643-669.
Epstein, L. and Wang, T.: 1994, ‘Intertemporal Asset Pricing under Knightian Uncertainty’, Econometrica 62, 283-322.
Gilboa, I., and Schmeidler, D.: 1989, ‘Maxmin Expected Utility with a Non-Unique Prior’, Journal of Mathematical Economics 18, 141-153.
Gilboa, I. and Schmeidler, D.: 1994, ‘Additive Representations of Non-Additive measures and the Choquet Integral’, Annals of Operations Research 52, 43-65.
Glosten, L. and Milgrom, P.: 1985, ‘Bid, Ask, and Transactions Prices in a Specialist Market with Heterogeneously Informed Traders’, Journal of Financial Economics 14, 71-100.
Hartigan, J.: 1983, Bayes Theory. New York: Springer-Verlag.
Kahneman, D. and Tversky, A.: 1974, ‘Judgement under Uncertainty: Heuristics and Biases’, Science 185, 1124-1131.
Kelsey, D. and Milne, F.: 1993, ‘Induced Preferences and Decision Making under Risk and Uncertainty’, University of Birmingham Discussion Paper.
Keynes, J.: 1921, A Treatise on Probability. London and New York: Macmillan & Co.
Klibanoff, P.: 1993, ‘Uncertainty, Decision and Normal Form Games’.
Knight, F.: 1921, Risk, Uncertainty and Profit. Boston and New York: Houghton-Miller
Kreps, D. and Wilson, R.: 1982, ‘Reputation and Imperfect Information’, Journal of Economic Theory 27, 253-279.
Kyburg, H. and Smokler, H.: 1980, Studies in Subjective Probability (2nd edition). New York: Robert E. Krieger Publishing Co.
Leamer, E.: 1986, ‘Bid Ask Spreads for Subjective Probabilities’, in Bayesian Inference and Decision Techniques, P. Goel and A. Zellner, Eds., Amsterdam: Elsevier Science Publishers.
LeRoy, S. and Singell, L.: 1987, ‘Knight on Risk and Uncertainty’, Journal of Political Economy 95, 394-406.
Lo, K.: 1995, ‘Equilibrium in Beliefs under Uncertainty’, University of Toronto.
Milgrom, P. and Roberts, J.: 1982, ‘Predation, Reputation and Entry Deterrence’, Journal of Economic Theory 27, 280-312.
Milgrom, P. and Roberts, J.: 1990, ‘Rationalizability, Learning and Equilibrium in Games with Strategic Complementarities’, Econometrica 58, 1255-1278.
Milgrom, P. and Shannon, C.: 1994, ‘Monotone Comparative Statics’, Econometrica 62, 157-180.
Milgrom, P. and Stokey, N.: 1982, ‘Information, Trade and Common Knowledge’, Journal of Economic Theory 26, 17-27.
Morris, S.: 1992, ‘Acceptance Games and Protocols’, CARESS Working Paper No. 92-22, University of Pennsylvania.
Morris, S.: 1993, ‘Bid Ask Spreads with Two Sided Private Information’, CARESS Working Paper No. 93-09, University of Pennsylvania.
Morris, S.: 1994, ‘Trade with heterogeneous prior beliefs and asymmetric information’, Econometrica 62, 1327-1347.
Mukerji, S.: 1994a, ‘Foundations of Decision Making under Subjective Uncertainty and Ambiguity: An Epistemic Approach’, Yale University, forthcoming in Economic Theory.
Mukerji, S.: 1994b, ‘A Theory of Play for Games in Strategic Form When Rationality is not Common Knowledge’, Yale University.
Ramsey, F.: 1926, ‘Truth and Probability’, reprinted in Kyburg and Smokler (1980), pp. 23-52.
Savage, L.: 1954, The Foundations of Statistics. John Wiley and Sons.
Schmeidler, D.: 1989, ‘Subjective Probability and Expected Utility Without Additivity’, Econometrica 57, 571-587.
Sebenius, J. and Geanakoplos, J.: 1983, ‘Don’t Bet On It: Contingent Agreements with Asymmetric Information’, Journal of the American Statistical Association 78, 424-426.
Shin, H.: 1991, ‘Optimal Betting Odds Against Insider Traders’, Economic Journal 101, 1179-1185.
Shin, H.: 1992, ‘Prices of State Contingent Claims with Insider Traders, and the Favourite-Longshot Bias’, Economic Journal 102, 426-435.
Shin, H.: 1993, ‘Measuring the Incidence of Insider Trading in a Market for State-Contingent Claims’, Economic Journal 103, 1141-1153.
Thaler, R.: 1991, QuasiRational Economics. New York: Russell Sage Foundation.
Walley, P.: 1991, Statistical Reasoning with Imprecise Probabilities. NewYork: Chapman and Hall.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Morris, S. Risk, uncertainty and hidden information. Theory and Decision 42, 235–269 (1997). https://doi.org/10.1023/A:1017913032257
Issue Date:
DOI: https://doi.org/10.1023/A:1017913032257