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The Value of Information in Monotone Decision Problems

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  • Jonathan Levin
  • Susan Athey

Abstract

February 2001 This paper studies decision problems under uncertainty where a decision-maker observes an imperfect signal about the true state of the world. We analyze the information preferences and information demand of such decision-makers, based on properties of their payoff functions. We restrict attention to "monotone decision problems," whereby the posterior beliefs induced by the signal can be ordered so that higher actions are chosen in response to higher signal realizations. Monotone decision problems are frequently encountered in economic modeling. We provide necessary and sufficient conditions for all decision makers with different classes of payoff functions to prefer one information structure to another. We also provide conditions under which two decision-makers in a given class can be ranked in terms of their marginal value for information and hence information demand. Applications and examples are given. Working Papers Index

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Paper provided by Stanford University, Department of Economics in its series Working Papers with number 01003.

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Date of creation: Feb 2001
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Handle: RePEc:wop:stanec:01003

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  1. Grant, S & Kajii, A & Polak, B, 1997. "Intrinsic Preference for Information," Papers 323, Australian National University - Department of Economics.
  2. Aghion, Philippe & Tirole, Jean, 1997. "Formal and Real Authority in Organizations," Journal of Political Economy, University of Chicago Press, vol. 105(1), pages 1-29, February.
  3. Jewitt, Ian, 1986. "A note on comparative statics and stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 249-254, June.
  4. Athey, S., 1996. "Characterizing Properties of Stochastic Objective Functions," Working papers 96-1, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
  6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  7. Athey, S, 1996. "Comparative Statics under Uncertainty : Single Crossing Properties and Log-Supermodularity," Working papers 96-22, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. Nicola Persico, 2000. "Information Acquisition in Auctions," Econometrica, Econometric Society, vol. 68(1), pages 135-148, January.
  9. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
  10. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  11. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
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