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Coalitional Manipulation on Networks

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  • Biung-Ghi Ju

    (Department of Economics, The University of Kansas)

Abstract

We consider an abstract model of division problems where each agent is identi- fied by a characteristic vector. Agents are situated on a network (a non-directed graph) and any connected coalition can reallocate members¡¯ characteristics (e.g. reallocation of claims in bankruptcy problems). A reallocation-proof rule prevents any coalition from benefiting, in terms of its total award, through a reallocation. We offer a full characterization of reallocation-proof rules without any assumption on the network structure. This result yields a variety of useful corollaries for specific networks such as the complete network, trees, networks without a ¡°bridge¡± etc. Our model has various special examples such as bankruptcy, surplus sharing, cost sharing, income redistribution, social choice with transferable utility, etc.

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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 200410.

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Length: 48 pages
Date of creation: Aug 2004
Date of revision: Aug 2004
Handle: RePEc:kan:wpaper:200410

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Keywords: Division problem; Coalitional manipulation; Network; Graph; Reallocationproofness;

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References

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  1. MORENO-TERNERO, Juan D., . "Proportionality and non-manipulability in bankruptcy problems," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1898, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, Elsevier, vol. 132(1), pages 1-26, January.
  3. 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, University of Kansas, Department of Economics 200307, University of Kansas, Department of Economics, revised Aug 2005.
  4. James Schummer, 1997. "Manipulation Through Bribes," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1207, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, Elsevier, vol. 2(4), pages 345-371, June.
  6. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, Econometric Society, vol. 60(5), pages 1009-37, September.
  7. Moulin, Herve, 1985. "Egalitarianism and Utilitarianism in Quasi-linear Bargaining," Econometrica, Econometric Society, Econometric Society, vol. 53(1), pages 49-67, January.
  8. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, Elsevier, vol. 45(3), pages 249-297, July.
  9. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, Elsevier, vol. 15(3), pages 231-246, June.
  10. Shigehiro Serizawa, 2006. "Pairwise Strategy-Proofness and Self-Enforcing Manipulation," Social Choice and Welfare, Springer, Springer, vol. 26(2), pages 305-331, April.
  11. Satterthwaite, Mark A & Sonnenschein, Hugo, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 48(4), pages 587-97, October.
  12. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154855, Tilburg University.
  13. Biung-Ghi Ju, 2003. "Manipulation via merging and splitting in claims problems," Review of Economic Design, Springer, Springer, vol. 8(2), pages 205-215, October.
  14. Juan D. Moreno-Ternero, 2007. "Bankruptcy Rules And Coalitional Manipulation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 105-118.
  15. Dominique Henriet & Herve' Moulin, 1996. "Traffic-Based Cost Allocation in a Network," RAND Journal of Economics, The RAND Corporation, vol. 27(2), pages 332-345, Summer.
  16. Juan D. Moreno-Ternero, 2007. "Erratum: "Bankruptcy Rules And Coalitional Manipulation"," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 411-424.
  17. John McMillan & Michael Rothschild & Robert Wilson, 1997. "Introduction," Journal of Economics & Management Strategy, Wiley Blackwell, Wiley Blackwell, vol. 6(3), pages 425-430, 09.
  18. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer, Springer, vol. 4(3), pages 255-272.
  19. Aadland, David & Kolpin, Van, 1998. "Shared irrigation costs: An empirical and axiomatic analysis," Mathematical Social Sciences, Elsevier, Elsevier, vol. 35(2), pages 203-218, March.
  20. Moulin, Herve, 1994. "Serial Cost-Sharing of Excludable Public Goods," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(2), pages 305-25, April.
  21. Chambers, Christopher P. & Thomson, William, 2002. "Group order preservation and the proportional rule for the adjudication of conflicting claims," Mathematical Social Sciences, Elsevier, Elsevier, vol. 44(3), pages 235-252, December.
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Cited by:
  1. 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, University of Kansas, Department of Economics 200307, University of Kansas, Department of Economics, revised Aug 2005.

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