Uncertainty

  • Peter J. Hammond
Part of the The New Palgrave book series (NPA)

Abstract

Nothing is more certain than the prevalence of uncertainty about the consequences of any economic decision. It is therefore entirely appropriate that uncertainty has been the subject of a large literature that grew out of important work in the early 1950s, and is still flourishing, as testified by the number of recent surveys and books such as Balch, McFadden and Wu (1974), Diamond and Rothschild (1978), Hirshleifer and Riley (1979), Lippman and McCall (1981), Fishburn (1982), Schoemaker (1982), Sinn ( 1983). No attempt will be made here to provide a comprehensive new survey. Rather, the devices of state contingent consequence functions and state preferences will be explained, and various types of uncertainty categorized. Following the pioneering work of Ramsey (1926), Savage (1954), and Anscombe and Aumann (1963) in particular, I shall discuss decision theory and when uncertainty can be described by subjective probabilities, based on an analysis of decision trees in the spirit of Raiffa (1968). While uncertainty per se can be largely treated through devices such as Debreu (1959) state contingent commodity contracts, the problems posed by asymmetric information and the lack of common knowledge are much more fundamental and intractable.

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Bibliography

  1. Anscombe, F.J. and Aumann, R.J. 1963. A definition of subjective probability. Annals of Mathematical Statistics 34, 199–205.CrossRefGoogle Scholar
  2. Arrow, K.J. 1951. Social Choice and Individual Values. New York: John Wiley; 2nd edn, New Haven: Yale University Press, 1963.Google Scholar
  3. Arrow, K.J. 1953, 1963. The rôle of securities in the optimal allocation of risk–bearing. Review of Economic Studies 31, 91–6; first published as ‘Le rôle des valeurs boursières pour la répartition la meilleure des risques’, Économetrie (Colloques Internationaux du Centre National de la Recherche Scientifique) 11, 41–7; reprinted as ch. 4 of Arrow (1971) and as ch. 3 of Arrow (1983).CrossRefGoogle Scholar
  4. Arrow, K.J. 1965. Aspects of the Theory of Risk–Bearing. Helsinki: Yrjö Jahnsson Foundation.Google Scholar
  5. Arrow, K.J. 1971. Essays in the Theory of Risk–Bearing. Amsterdam: North–Holland; Chicago: Markham.Google Scholar
  6. Arrow, K.J. 1983. Collected Papers of Kenneth J. Arrow, 2: General Equilibrium. Cambridge, Mass.: The Belknap Press of Harvard University Press.Google Scholar
  7. Balch, M., McFadden, D. and Wu, S. (eds) 1974. Essays on Economic Behavior under Uncertainty. Amsterdam: North-Holland.Google Scholar
  8. Bernoulli, D. 1738. Specimen theoriae novae de mensura sortis. Commentarii academiae scientiarum imperialis Petropolitanae 5, 175–92. Translated by L. Sommer (1954) as ‘Exposition of a new theory on the measurement of risk’, Econometrica 22, 23–36.Google Scholar
  9. Bolker, E.D. 1967. A simultaneous axiomatization of utility and subjective probability. Philosophy of Science 34, 333–40.CrossRefGoogle Scholar
  10. Border, K.C. 1985. More on Harsanyi’s utilitarian cardinal welfare theorem. Social Choice and Welfare 1, 279–81.CrossRefGoogle Scholar
  11. Cass, D. and Shell, K. 1983. Do sunspots matter? Journal of Political Economy 91,193–227.CrossRefGoogle Scholar
  12. Debreu, G. 1959. Theory of Value: An Axiomatic Analysis of General Equilibrium. New York: John Wiley.Google Scholar
  13. Diamond, P.A. 1967. The role of a stock market in a general equilibrium model with technological uncertainty. American Economic Review 57, 759–76.Google Scholar
  14. Diamond, P.A. and Rothschild, M. (eds) 1978. Uncertainty in Economics: Reading and Exercises. New York: Academic Press.Google Scholar
  15. Drèze, J.H. 1974. Axiomatic theories of choice, cardinal utility and subjective probability: A review. In Allocation under Uncertainty ed. J.H. Drèze, London: Macmillan, 3–23.CrossRefGoogle Scholar
  16. Ellsberg, D. 1961. Risk, ambiguity and the Savage axioms. Quarterly Journal of Economics 75, 643–69.CrossRefGoogle Scholar
  17. Fishburn, P.C. 1982. The Foundations of Expected Utility. Dordrecht: Reidel.CrossRefGoogle Scholar
  18. Gärdenfors, P. and Sahlin, N.-E. 1982. Unreliable probabilities, risk taking, and decision making. Synthèse 53, 361–86.CrossRefGoogle Scholar
  19. Hammond, P.J. 1983. Ex-post optimality as a dynamically consistent objective for collective choice under uncertainty. In Social Choice and Welfare, ed. P.K. Pattanaik and M. Salles, Amsterdam: North–Holland, 175–205.CrossRefGoogle Scholar
  20. Harsanyi, J.C. 1955. Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. Journal of Political Economy 63, 309–21.CrossRefGoogle Scholar
  21. Harsanyi, J.C. 1967, 1968. Games with incomplete information played by ‘Bayesian’ players, I–III. Management Science; Theory 14, 159–82, 320–34 and 486–502.CrossRefGoogle Scholar
  22. Harsanyi, J.C. 1975. Nonlinear social welfare functions: do welfare economists have a special exemption from Bayesian rationality? Theory and Decision 6, 311–32.CrossRefGoogle Scholar
  23. Harsanyi, J.C. 1978. Bayesian decision theory and utilitarian ethics. American Economic Review, Papers and Proceedings 68, 223–8.Google Scholar
  24. Hausner, M. 1954. Multidimensional utilities. In R.M. Thrall et al. (eds) (1954), 167–90.Google Scholar
  25. Herstein, I.N. and Milnor, J. 1953. An axiomatic approach to measurable utility. Econometrica 21, 291–7.CrossRefGoogle Scholar
  26. Hirshleifer, 1966. Investment decision under uncertainty: applications of the state-preference approach. Quarterly Journal of Economics 80, 252–77.CrossRefGoogle Scholar
  27. Hirshleifer, J. and Riley, J.G. 1979. The analysis of uncertainty and information: an expository survey. Journal of Economic Literature 17, 1375–421.Google Scholar
  28. Jeffrey, R.C. 1965. The Logic of Decision. New York: McGraw–Hill.Google Scholar
  29. Jeffrey, R.C. 1974. Frameworks for preference. In Balch, McFaddên and Wu (1974), 74–9.Google Scholar
  30. Jones-Lee, M.W. 1979. The expected conditional utility theorem for the case of personal probabilities and state conditional utility functions: a proof and some notes. Economic Journal 89, 834–49.CrossRefGoogle Scholar
  31. Kami, E., Schmeidler, D. and Vind, K. 1983. On state dependent preferences and subjective probabilities. Econometrica 51, 1021–31.CrossRefGoogle Scholar
  32. Keynes, J.M. 1921. A Treatise on Probability. London: Macmillan; New York: Harper & Row, 1962.Google Scholar
  33. Knight, F.H. 1921,1911. Risk, Uncertainty and Profit. Chicago: University of Chicago Press.Google Scholar
  34. Kyburg, H.E., Jr and Smokier, H.E. (eds) 1964. Studies in Subjective Probability. New York: John Wiley.Google Scholar
  35. Lippman, S.A. and McCall, J.J. 1981. The economics of uncertainty: selected topics and probabilistic methods. In Handbook of Mathematical Economics, Vol. 1, ed. K.J. Arrow and M.D. Intriligator, Amsterdam: North–Holland, 211–84.Google Scholar
  36. Machina, M. 1982. ‘Expected utility’ analysis without the independence axiom. Econometrica 50, 277–323.CrossRefGoogle Scholar
  37. Mertens, J.-F. and Zamir, S. 1985. Formalization of Harsanyi’s notions of ‘type’ and ‘consistency’ in games with incomplete information. International Journal of Game Theory 14, 1–29.CrossRefGoogle Scholar
  38. Myerson, R.B. 1979. An axiomatic derivation of subjective probability, utility and evaluation functions. Theory and Decision 11, 339–52.CrossRefGoogle Scholar
  39. Raina, H. 1968. Decision Analysis: Introductory Lectures on Choices under Uncertainty. Reading, Mass.: Addison–Wesley.Google Scholar
  40. Ramsey, F.P. 1926. Truth and probability. In F.P. Ramsey, The Foundations of Mathematics and Other Logical Essays, ed. R.B. Braithwaite, New York: Humanities Press, 1950, and in Kyburg and Smokier (1964).Google Scholar
  41. Samuelson, P.A. 1952. Probability, utility and the independence axiom. Econometrica 20, 670–78.CrossRefGoogle Scholar
  42. Savage, L.J. 1954. The Foundations of Statistics. New York: John Wiley, and Dover. 2nd revised edn, 1972.Google Scholar
  43. Schoemaker, P.J.H. 1982. The expected utility model: its variants, purposes, evidence and limitations. Journal of Economic Literature 20, 529–63.Google Scholar
  44. Sinn, H.-W. 1983. Economic Decisions Under Uncertainty. Amsterdam: North-Holland.Google Scholar
  45. Skala, H.J. 1975. Non-Archimedean Utility Theory. Dordrecht: D. Reidel.CrossRefGoogle Scholar
  46. Starr, R. 1973. Optimal production and allocation under uncertainty. Quarterly Journal of Economics 87, 668–90.CrossRefGoogle Scholar
  47. Thrall, R.M. 1954. Applications of multidimensional utility theory. In R.M. Thrall et al. (eds), 181–6.Google Scholar
  48. Thrall, R.M., Coombs, CH. and Davis, R.L. (eds) 1954. Decision Processes. New York: John Wiley.Google Scholar
  49. Weller, P.A. 1978. Consistent intertemporal decision making under uncertainty. Review of Economic Studies 45, 263–6.CrossRefGoogle Scholar
  50. Wilson, R.B. 1968. The theory of syndicates. Econometrica 36, 119–32.CrossRefGoogle Scholar

Copyright information

© Palgrave Macmillan, a division of Macmillan Publishers Limited 1990

Authors and Affiliations

  • Peter J. Hammond

There are no affiliations available

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