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Strategy-Proof Risk Sharing

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  • Biung-Ghi Ju

    (Department of Economics, The University of Kansas)

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    Abstract

    We consider risk sharing problems with a single good and ?nite number of states. Agents have a common prior and their preferences are represented in the expected utility form and are risk averse. We study efficient and individually rational risk sharing rules satisfying strategy-proofness, the requirement that no one can ever be bene?ted by misrepresenting his preference. When aggregate certainty holds, we show that ¡°?xed price selections¡± from the Walrasian correspondence are the only rules satisfying efficiency, individual rationality, and strategy-proofness. However, when aggregate uncertainty holds, we show that there exists no rule satisfying the three requirements. Moreover, in the two agents case, we show that dictatorial rules are the only efficient and strategy-proof rules. Dropping the common prior assumption in the model, we show that this assumption is necessary and sufficient for the existence of rules satisfying the three main requirements in the two agents and aggregate certainty case.

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    File URL: http://www.ku.edu/~bgju/2003Papers/200305Ju.pdf
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    Bibliographic Info

    Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 200305.

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    Length: 37 pages
    Date of creation: Apr 2003
    Date of revision: Apr 2003
    Handle: RePEc:kan:wpaper:200305

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    Related research

    Keywords: Risk sharing; strategy-proofness; efficiency; individual rationality.;

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    1. James Schummer, 1996. "Strategy-proofness versus efficiency on restricted domains of exchange economies," Social Choice and Welfare, Springer, vol. 14(1), pages 47-56.
    2. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    3. Sobel, Joel, 1998. "Manipulation of Preferences and Relative Utilitarianism," University of California at San Diego, Economics Working Paper Series qt1x32m32n, Department of Economics, UC San Diego.
    4. McKelvey, Richard D & Page, Talbot, 1986. "Common Knowledge, Consensus, and Aggregate Information," Econometrica, Econometric Society, vol. 54(1), pages 109-27, January.
    5. Thomson, William, 1984. "The Manipulability of Resource Allocation Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 51(3), pages 447-60, July.
    6. Billot, A. & Chateauneuf, A. & Gilboa, I. & Tallon, J.-M., 1998. "Sharing Beliefs: Between Agreeing and Disagreeing," Papiers d'Economie Mathématique et Applications 98.30, Université Panthéon-Sorbonne (Paris 1).
    7. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    8. Bacharach, Michael, 1985. "Some extensions of a claim of Aumann in an axiomatic model of knowledge," Journal of Economic Theory, Elsevier, vol. 37(1), pages 167-190, October.
    9. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
    10. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
    11. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    12. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
    13. Hurwicz, L, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 217-25, April.
    14. MANIQUET, François & SPRUMONT, Yves, 1998. "Efficient Strategy-Proof Allocation Functions in Linear Production Economies," Cahiers de recherche 9805, Universite de Montreal, Departement de sciences economiques.
    15. Shigehiro Serizawa & John A. Weymark, 2002. "Efficient Strategy-Proof Exchange and Minimum Consumption Guarantees," Vanderbilt University Department of Economics Working Papers 0216, Vanderbilt University Department of Economics, revised Aug 2002.
    16. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
    17. Lin Zhou, 1990. "Inefficiency of Strategy-Proof Allocation Mechanisms in Pure Exchange Economies," Cowles Foundation Discussion Papers 954, Cowles Foundation for Research in Economics, Yale University.
    18. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January.
    19. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
    20. Serizawa, Shigehiro, 2002. "Inefficiency of Strategy-Proof Rules for Pure Exchange Economies," Journal of Economic Theory, Elsevier, vol. 106(2), pages 219-241, October.
    21. Satterthwaite, Mark A & Sonnenschein, Hugo, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Wiley Blackwell, vol. 48(4), pages 587-97, October.
    22. 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.
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    25. Benassy, Jean-Pascal, 1986. "On Competitive Market Mechanisms," Econometrica, Econometric Society, vol. 54(1), pages 95-108, January.
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