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Coalitional Manipulation on Communication Network

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  • Biung-Ghi Ju

Abstract

In an abstract model of division problems, we study division rules that are not manipulable through a reallocation of individual characteristic vectors within a coalition (e.g. reallocation of claims in bankruptcy problems). A coalition can be formed if members of the coalition are connected on a communication network, or a graph. We offer a characterization of non-manipulable division rules without any assumption on the structure of communication network. As corollaries, we obtain a number of earlier characterization results established with the assumption of complete network (complete graph) in various specialized settings. Moreover, our characterization, as we show, can be quite different from the earlier results depending on the network structure: for example, when the network is a tree, much larger family of rules are shown to be non-manipulable. The abstract model we consider can have various special examples such as bankruptcy problems, surplus sharing problems, cost sharing problems, social choice with transferable utility, etc

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 Far Eastern Meetings with number 563.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:feam04:563

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Keywords: Division problem; Coalitional manipulation; Non-manipulability; Reallocation-proofness; Non-bossiness; Network;

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References

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  1. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer, vol. 4(3), pages 255-272.
  2. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  3. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
  4. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
  5. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
  6. Juan D. Moreno-Ternero, 2007. "Bankruptcy Rules And Coalitional Manipulation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 105-118.
  7. Chambers, Christopher P. & Thomson, William, 2002. "Group order preservation and the proportional rule for the adjudication of conflicting claims," Mathematical Social Sciences, Elsevier, vol. 44(3), pages 235-252, December.
  8. Moulin Herve, 1984. "Egalitarianisme and utilitarianism in quasi-linear bargaining," CEPREMAP Working Papers (Couverture Orange) 8417, CEPREMAP.
  9. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
  10. 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.
  11. Biung-Ghi Ju & Eiichi Miyagawa & Toyotaka Sakai, 2003. "Non-Manipulable Division Rules in Claim Problems and Generalizations," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200307, University of Kansas, Department of Economics, revised Aug 2005.
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