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Contracting for Innovation under Knightian Uncertainty

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  • Massimiliano Amarante
  • Mario Ghossoub
  • Edmund Phelps

Abstract

At any given point in time, the collection of assets existing in the economy is observable. Each asset is a function of a set of contingencies. The union taken over all assets of these contingencies is what we call the set of publicly known states. An innovation is a set of states that are not publicly known along with an asset (in a broad sense) that pays contingent on those states. The creator of an innovation is an entrepreneur. He is represented by a probability measure on the set of new states. All other agents perceive the innovation as ambiguous: each of them is represented by a set of probabilities on the new states. The agents in the economy are classified with respect to their attitude towards this Ambiguity: the financiers are (locally) Ambiguity-seeking while the consumers are Ambiguity-averse. An entrepreneur and a financier come together when the former seeks funds to implement his project and the latter seeks new profit opportunities. The resulting contracting problem does not fall within the standard theory due to the presence of Ambiguity (on the financier’s side) and to the heterogeneity in the parties’ beliefs. We prove existence and monotonicity (i.e., truthful revelation) of an optimal contract. We characterize such a contract under the additional assumption that the financiers are globally Ambiguity-seeking. Finally, we re-formulate our results in an insurance framework and extend the classical result of Arrow [4] and the more recent one of Ghossoub [24]. In the case of an Ambiguity-averse insurer, we also show that an optimal contract has the form of a generalized deductible.

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Bibliographic Info

Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 18-2012.

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Length: 41 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:mtl:montec:18-2012

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Keywords: Innovation; Entrepreneurship; Knightian Uncertanity; Ambiguity; Contracting; Vigilance; Insurance;

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References

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  1. Dana, Rose-Anne & Carlier, Guillaume, 2011. "Optimal Demand for Contingent Claims when Agents have law Invariant Utilities," Economics Papers from University Paris Dauphine 123456789/2317, Paris Dauphine University.
  2. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  3. Mukerji, Sujoy, 1998. "Ambiguity Aversion and Incompleteness of Contractual Form," American Economic Review, American Economic Association, vol. 88(5), pages 1207-31, December.
  4. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
  5. Boldrin, Michele & Levine, David K., 2008. "Perfectly competitive innovation," Journal of Monetary Economics, Elsevier, vol. 55(3), pages 435-453, April.
  6. Sujoy Mukerji & Jean-Marc Tallon, 2003. "An overview of economic applications of David Schmeidler`s models of decision making under uncertainty," Economics Series Working Papers 165, University of Oxford, Department of Economics.
  7. Carlier, G. & Dana, R.-A., 2005. "Rearrangement inequalities in non-convex insurance models," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 483-503, August.
  8. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
  9. Tallon, Jean-Marc & Dana, Rose-Anne & Chateauneuf, Alain, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Economics Papers from University Paris Dauphine 123456789/5461, Paris Dauphine University.
  10. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  11. Carlier, Guillaume & Dana, Rose-Anne, 2005. "Rearrangement inequalities in non-convex insurance models," Economics Papers from University Paris Dauphine 123456789/5389, Paris Dauphine University.
  12. repec:hal:cesptp:halshs-00451997 is not listed on IDEAS
  13. Carlier, G. & Dana, R. A., 2003. "Core of convex distortions of a probability," Journal of Economic Theory, Elsevier, vol. 113(2), pages 199-222, December.
  14. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426.
  15. Dana, Rose-Anne, 2002. "On Equilibria when Agents Have Multiple Priors," Economics Papers from University Paris Dauphine 123456789/5456, Paris Dauphine University.
  16. Carlier, Guillaume & Dana, Rose-Anne, 2003. "Core of convex distortions of a probability," Economics Papers from University Paris Dauphine 123456789/5446, Paris Dauphine University.
  17. Paul M Romer, 1999. "Increasing Returns and Long-Run Growth," Levine's Working Paper Archive 2232, David K. Levine.
  18. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  19. repec:hal:journl:halshs-00451997 is not listed on IDEAS
  20. Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
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