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The price for information about probabilities and its relation with risk and ambiguity

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In this article, ambiguity attitude is measured through the maximum price a decision maker is willing to pay to know the probability of an event. Two problems are examined in which the decision maker faces an act: in one case, buying information implies playing a lottery, while, in the other case, buying information gives also the option to avoid playing the lottery. In both decision settings, relying on the Choquet expected utility model, we study how the decision maker’s risk and ambiguity attitudes affect the reservation price for ambiguity resolution. These effects are analyzed for different levels of ambiguity of the act. Operating instructions for the elicitation of the reservation price for ambiguity resolution in an experimental setting are provided at the end of the article.

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  1. Abdellaoui, M., Baillon, A., Placido, L., & Wakker, P. (2011). The rich domain of uncertainty: Source functions and their experimental implementation. American Economic Review, 5, 101, 695–723.

  2. Ahn, D., Choi, S., Gale, D., & Kariv, S. (2010). Estimating ambiguity aversion in a portfolio choice experiment. Los Angeles: mimeo, University of California.

  3. Andersen, S., Fountain, J., Harrison, G. W., & Rutström, E. E. (2009). Estimating aversion to uncertainty. mimeo, University of Central Florida.

  4. Baillon, A., & Bleichrodt, H. (2010). Are subjective probabilities sign-dependent? mimeo, Erasmus University Rotterdam.

  5. Becker S. W., Brownson F. O. (1964) What price ambiguity? Or the role of ambiguity in decision making. Journal of Political Economy 72: 62–73

  6. Becker G. M., DeGroot M. H., Marschak J. (1964) Measuring utility by a single-response sequential method. Behavioral Science 9: 226–232

  7. Camerer C. F. (1995) Individual decision making. In: Kagel J., Roth A. (eds) Handbook of experimental economics. Princeton University Press, Princeton, pp 587–703

  8. Camerer C., Weber M. (1992) Recent developments in modeling preferences: Uncertainty and ambiguity. Journal of Risk and Uncertainty 5: 325–370

  9. Dominiak, A., & Schnedler, W. (2010). Attitudes toward uncertainty and randomization: An experimental study. mimeo, University of Heidelberg.

  10. Ellsberg D. (1961) Risk, ambiguity and the Savage axioms. Quarterly Journal of Economics 75: 643–669

  11. Fellner W. (1961) Distortion of subjective probabilities as a reaction to uncertainty. Quarterly Journal of Economics 75: 670–689

  12. Ghirardato P. (2004) Defining ambiguity and ambiguity attitude. In: Gilboa I. (Ed.) Uncertainty in economic theory: A collection of essays in honor of David Schmeidler’s 65th birthday. Routledge, London, pp 36–45

  13. Gilboa I., Schmeidler D. (1989) Maxmin expected utility with non-unique prior. Journal of Mathematical Economics 18: 141–153

  14. Halevy Y. (2007) Ellsberg revisited: An experimental study. Econometrica 75: 503–536

  15. Harrison G. W. (1994) Expected utility theory and the experimentalists. Empirical Economics 19: 223–253

  16. Harrison G. W., Rutström E. E. (2008) Risk aversion in the laboratory. In: Harrison G. W., Cox J. (eds) Risk aversion in experiments. JAI Press, Bradford, UK, pp 41–196

  17. Harrison G. W., Rutström E. E. (2009) Expected utility theory and prospect theory: One wedding and a decent funeral. Experimental Economics 12: 133–158

  18. Harrison G. W., Johnson E., McInnes M. M., Rutström E. E. (2007) Measurement with experimental controls. In: Boumans M. (Ed.) Measurement in economics: A handbook. Elsevier, San Diego, CA, pp 79–104

  19. Heath C., Tversky A. (1991) Preference and belief: Ambiguity and competence in choice under uncertainty. Journal of Risk and Uncertainty 4: 5–28

  20. Hey, J. D., Lotito, G., & Maffioletti, A. (2007). Choquet OK? mimeo, University of York.

  21. Hey J. D., Lotito G., Maffioletti A. (2010) The descriptive and predictive adequacy of theories of decision making under uncertainty/ambiguity. Journal of Risk and Uncertainty 41: 81–111

  22. Hey J. D., Orme C. (1994) Investigating generalizations of expected utility theory using experimental data. Econometrica 62: 1291–1326

  23. Holt C. A. (1986) Preference reversal and the independence axiom. American Economic Review 76: 508–515

  24. Ivanov A. (2011) Attitudes to ambiguity in one-shot normal-form games: An experimental study. Games and Economic Behavior 71: 366–394

  25. Izhakian, Y., & Benninga, S. (2008). The uncertainty premium in an ambiguous economy. mimeo, Tel Aviv University.

  26. Karni E., Safra Z. (1987) ‘Preference reversal’ and the observability of preferences by experimental methods. Econometrica 55: 675–685

  27. Klibanoff P., Marinacci M., Mukerji S. (2005) A smooth model of decision making under ambiguity. Econometrica 73: 1849–1892

  28. Knight F. (1921) Risk, uncertainty, and profit. Houghton Mifflin, Boston

  29. Luce, R. D., & Suppes, P. (1965). Preference, utility, and subjective probability. In: R. D. Luce, R. R. Bush, & E. Galanter (Eds.), Handbook of mathematical psychology (Vol. 3, pp 252–410). New York: Wiley.

  30. Maccheroni F., Marinacci M., Rustichini A. (2006) Ambiguity aversion, robustness, and the variational representation of preferences. Econometrica 74: 1447–1498

  31. Maccheroni, F., Marinacci, M., & Ruffino, D. (2010). Robust mean-variance portfolio analysis. Milan: mimeo, Bocconi University.

  32. Machina M. J. (2004) Almost-objective uncertainty. Economic Theory 1: 1–54

  33. Montesano A. (1988) The risk aversion measure without the independence axiom. Theory and Decision 24: 269–288

  34. Montesano A. (1991) Measures of risk aversion with expected and nonexpected utility. Journal of Risk and Uncertainty 4: 271–283

  35. Montesano A., Giovannoni F. (1996) Uncertainty aversion and aversion to increasing uncertainty. Theory and Decision 41: 133–148

  36. Nau R. F. (2006) Uncertainty aversion with second-order utilities and probabilities. Management Science 52: 136–145

  37. Plott C. R., Zeiler K. (2005) The willingness to pay-willingness to accept gap, the ‘endowment effect,’ subject misconceptions, and experimental procedures for eliciting valuations. American Economic Review 95: 530–545

  38. Quiggin J. (2007) Ambiguity and the value of information: An almost-objective events analysis. Economic Theory 30: 409–414

  39. Savage L. J. (1954) The foundations of statistics. Wiley, New York

  40. Schmeidler D. (1989) Subjective probability and expected utility without additivity. Econometrica 57: 571–587

  41. Schoemaker P. (1982) The expected utility model: Its variants, purposes, evidence and limitations. Journal of Economic Literature 20: 529–563

  42. Skiadas, C. (2009). Smooth ambiguity toward small risks and continuous-time recursive utility. mimeo, Northwestern University.

  43. Snow A. (2010) Ambiguity and the value of information. Journal of Risk and Uncertainty 40: 133–145

  44. Starmer C. (2000) Developments in non-expected utility theory: The hunt for a descriptive theory of choice under risk. Journal of Economic Literature 38: 332–382

  45. Wakker P. P. (2010) Prospect theory: For risk and ambiguity. Cambridge University Press, Cambridge, UK

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Correspondence to Giuseppe Attanasi.

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Attanasi, G., Montesano, A. The price for information about probabilities and its relation with risk and ambiguity. Theory Decis 73, 125–160 (2012). https://doi.org/10.1007/s11238-011-9271-6

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  • Ambiguity aversion
  • Choquet expected utility
  • Information about probabilities
  • Reservation price for ambiguity resolution
  • Option value

JEL Classification

  • D81
  • D83
  • C91