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Efficient Compromising

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  • Tilman Börgers
  • Peter Postl

Abstract

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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Bibliographic Info

Paper provided by Department of Economics, University of Birmingham in its series Discussion Papers with number 06-11R.

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Length: 37 pages
Date of creation: Jun 2008
Date of revision:
Handle: RePEc:bir:birmec:06-11r

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Postal: Edgbaston, Birmingham, B15 2TT
Web page: http://www.economics.bham.ac.uk
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Related research

Keywords: arbitration; mechanism design without transferrable utility;

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  5. 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.
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  9. 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.
  10. Martin F. Hellwig, 2003. "Public-Good Provision with Many Participants," Review of Economic Studies, Wiley Blackwell, vol. 70(3), pages 589-614, 07.
  11. 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.
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Citations

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Cited by:
  1. Rafael Hortala-Vallve, 2007. "Inefficiencies on Linking Decisions," Economics Series Working Papers 321, University of Oxford, Department of Economics.
  2. Hanming Fang & Peter Norman, 2005. "Overcoming Participation Constraints," Cowles Foundation Discussion Papers 1511R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2006.
  3. Schmitz, Patrick W. & Tröger, Thomas, 2011. "The (sub-)optimality of the majority rule," MPRA Paper 32716, University Library of Munich, Germany.
  4. Postl, Peter, 2013. "A ‘divide and choose’ approach to compromising," Economics Letters, Elsevier, vol. 119(2), pages 204-209.
  5. Börgers, Tilman & Smith, Doug, 2014. "Robust mechanism design and dominant strategy voting rules," Theoretical Economics, Econometric Society, vol. 9(2), May.
  6. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Mechanism Design without Money," Working Papers tecipa-481, University of Toronto, Department of Economics.
  7. Jose Apesteguia & Miguel A. Ballester & Rosa Ferrer, 2006. "On the justice of voting systems," Economics Working Papers 987, Department of Economics and Business, Universitat Pompeu Fabra.
  8. Giles, Adam & Postl, Peter, 2014. "Equilibrium and effectiveness of two-parameter scoring rules," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 31-52.

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