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Contracting for Innovation under Knightian Uncertainty
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Contracting for Innovation under Knightian Uncertainty

Author

Listed:
  • 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.

Suggested Citation

  • Massimiliano Amarante & Mario Ghossoub & Edmund Phelps, 2012. "Contracting for Innovation under Knightian Uncertainty," Cahiers de recherche 18-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:18-2012
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    References listed on IDEAS

    as
    1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. Boldrin, Michele & Levine, David K., 2008. "Perfectly competitive innovation," Journal of Monetary Economics, Elsevier, vol. 55(3), pages 435-453, April.
    3. repec:dau:papers:123456789/2348 is not listed on IDEAS
    4. 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.
    5. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    6. Rose-Anne Dana, 2002. "On Equilibria when Agents Have Multiple Priors," Annals of Operations Research, Springer, vol. 114(1), pages 105-115, August.
    7. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
    8. Itzhak Gilboa & Massimo Marinacci, 2011. "Ambiguity and the Bayesian Paradigm," Working Papers 379, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    9. repec:dau:papers:123456789/5446 is not listed on IDEAS
    10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    11. 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.
    12. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    13. Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
    14. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    15. repec:dau:papers:123456789/5389 is not listed on IDEAS
    16. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
    17. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    18. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    19. repec:dau:papers:123456789/2317 is not listed on IDEAS
    20. repec:dau:papers:123456789/5456 is not listed on IDEAS
    21. Reinganum, Jennifer F., 1989. "The timing of innovation: Research, development, and diffusion," Handbook of Industrial Organization, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 14, pages 849-908, Elsevier.
    22. repec:dau:papers:123456789/5461 is not listed on IDEAS
    23. repec:dau:papers:123456789/5394 is not listed on IDEAS
    24. R. Schmalensee & R. Willig (ed.), 1989. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 1, number 1.
    25. G. Carlier & R. Dana, 2008. "Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 189-223, August.
    26. Sujoy Mukerji & Jean-Marc Tallon & EUREQua & CNRS - Universite Paris I., 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.
    27. Paolo Ghirardato & Marciano Siniscalchi, 2010. "A more robust definition of multiple priors," Carlo Alberto Notebooks 144, Collegio Carlo Alberto.
    28. Guillaume Carlier & Rose-Anne Dana, 2003. "Pareto efficient insurance contracts when the insurer's cost function is discontinuous," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 871-893, June.
    29. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
    30. Mukerji, Sujoy, 1998. "Ambiguity Aversion and Incompleteness of Contractual Form," American Economic Review, American Economic Association, vol. 88(5), pages 1207-1231, December.
    31. Itzhak Gilboa, 2004. "Uncertainty in Economic Theory," Post-Print hal-00756317, HAL.
    32. R. Schmalensee & R. Willig (ed.), 1989. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 2, number 2.
    33. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    34. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, July.
    35. 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.
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    Citations

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    Cited by:

    1. Swagata Bhattacharjee, 2019. "Dynamic Contracting for Innovation Under Ambiguity," Working Papers 1022, Ashoka University, Department of Economics, revised Aug 2019.
    2. Ghossoub, Mario, 2015. "Vigilant measures of risk and the demand for contingent claims," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 27-35.
    3. Bhattacharjee, Swagata, 2022. "Dynamic contracting for innovation under ambiguity," Games and Economic Behavior, Elsevier, vol. 132(C), pages 534-552.

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    More about this item

    Keywords

    Innovation; Entrepreneurship; Knightian Uncertanity; Ambiguity; Contracting; Vigilance; Insurance;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • L26 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Entrepreneurship
    • P19 - Political Economy and Comparative Economic Systems - - Capitalist Economies - - - Other

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