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Efficient Compromising

  • Tilman Börgers
  • Peter Postl

Two agents have to choose one of three alternatives. Their ordinal rankings of these alternatives are commonly known among them. The rankings are diametrically opposed to each other. Ex-ante efficiency requires that they reach a compromise, that is choose the alternative which they both rank second, if and only if the weighed sum of their von Neumann Morgenstern utilities from this alternative exceeds the weighted sum of utilities when either agent's most preferred alternative is chosen. We assume that the von Neumann Morgenstern utilities from this alternative exceeds the weighted sum of utilities when either agent's most preferred alternative is chosen. We ssume that the von Neumann Morgenstern utilities of the middle ranked alternative are independent and identically distributed, privately observed random variables, and ask whether there are incentive compatible decision rules which elicit utilities and implement efficient decisions. We show that no such decision rules exist if the distribution of agents' types has a density with full support. We also study the problem of finding second-best decision rules in our set-up, and explain how this problem differs from more familiar second-best problems. We give analytical and numberical insights into the nature of second-best rules. The compromise problem studied in this paper is closely related to a public goods problem in which individual agents face a liquidity constraint, but no participation constraint needs to be satisfied.

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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 784828000000000188.

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Date of creation: 05 Jul 2005
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Handle: RePEc:cla:levrem:784828000000000188
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  1. Roger B. Myerson & Mark A. Satterthwaite, 1981. "Efficient Mechanisms for Bilateral Trading," Discussion Papers 469S, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Werner Güth & Martin Hellwig, 1986. "The private supply of a public good," Journal of Economics, Springer, vol. 5(1), pages 121-159, December.
  3. Bengt Holmstrom & Roger B. Myerson, 1981. "Efficient and Durable Decision Rules with Incomplete Information," Discussion Papers 495, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Bhaskar Dutta & Hans Peters & Arunava Sen, 2007. "Strategy-proof Cardinal Decision Schemes," Social Choice and Welfare, Springer, vol. 28(1), pages 163-179, January.
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  6. Border, Kim C, 1991. "Implementation of Reduced Form Auctions: A Geometric Approach," Econometrica, Econometric Society, vol. 59(4), pages 1175-87, July.
  7. 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.
  8. repec:cup:cbooks:9780521551847 is not listed on IDEAS
  9. Matthew O Jackson & Hugo F Sonnenschein, 2007. "Overcoming Incentive Constraints by Linking Decisions -super-1," Econometrica, Econometric Society, vol. 75(1), pages 241-257, 01.
  10. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  11. Rob, Rafael, 1989. "Pollution claim settlements under private information," Journal of Economic Theory, Elsevier, vol. 47(2), pages 307-333, April.
  12. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-61, March.
  13. Cramton, Peter & Gibbons, Robert & Klemperer, Paul, 1987. "Dissolving a Partnership Efficiently," Econometrica, Econometric Society, vol. 55(3), pages 615-32, May.
  14. Mailath, George J & Postlewaite, Andrew, 1990. "Asymmetric Information Bargaining Problems with Many Agents," Review of Economic Studies, Wiley Blackwell, vol. 57(3), pages 351-67, July.
  15. repec:cup:cbooks:9780521536721 is not listed on IDEAS
  16. d'Aspremont, Claude & Gerard-Varet, Louis-Andre, 1979. "Incentives and incomplete information," Journal of Public Economics, Elsevier, vol. 11(1), pages 25-45, February.
  17. Martin F. Hellwig, 2003. "Public-Good Provision with Many Participants," Review of Economic Studies, Wiley Blackwell, vol. 70(3), pages 589-614, 07.
  18. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
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