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

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Abstract

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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References

  • 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.

    Google Scholar 

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

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

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

  • 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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Chapter  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Google Scholar 

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

    Article  Google Scholar 

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

  • 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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • 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.

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

    Article  Google Scholar 

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

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

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

    Google Scholar 

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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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