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Manipulation Through Bribes

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  • James Schummer

Abstract

We consider allocation rules that choose both a public outcome and transfers, based on the agents' reported valuations of the outcomes. Under a given allocation rule, a bribing situation exists when one agent could pay another to misreport his valuations, resulting in a net gain to both agents. A rule is bribe-proof if such opportunities never arise (including the case in which the briber and bribee are the same agent). The central result is that under a bribe-proof rule, regardless of the domain of admissible valuations, the payoff to any one agent is a continuous function of any other agent's reported valuations. We then show that on connected domains of valuation functions, if either the set of outcomes is finite or each agent's set of admissible valuations is smoothly connected, then an agent's payoff is a constant function of other agents' reported valuations. Finally, under the additional assumption of a standard richness condition on the set of admissible valuations, a bribe-proof rule must be a constant function.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1207.

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Date of creation: Jun 1997
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Handle: RePEc:nwu:cmsems:1207

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  1. G. Chichilnisky & G. M. Heal, 1997. "The geometry of implementation: a necessary and sufficient condition for straightforward games (*)," Social Choice and Welfare, Springer, vol. 14(2), pages 259-294.
  2. Green, Jerry & Laffont, Jean-Jacques, 1979. "On Coalition Incentive Compatibility," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 243-54, April.
  3. Schummer, James, 2000. "Eliciting Preferences to Assign Positions and Compensation," Games and Economic Behavior, Elsevier, vol. 30(2), pages 293-318, February.
  4. Cremer, Jacques, 1996. "Manipulations by Coalitions Under Asymmetric Information: The Case of Groves Mechanisms," Games and Economic Behavior, Elsevier, vol. 13(1), pages 39-73, March.
  5. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, Econometric Society, vol. 41(4), pages 617-31, July.
  6. Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, Econometric Society, vol. 45(2), pages 427-38, March.
  7. Salvador Barbera & Matthew O. Jackson, 1993. "Strategy-Proof Exchange," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1021, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Holmstrom, Bengt, 1979. "Groves' Scheme on Restricted Domains," Econometrica, Econometric Society, Econometric Society, vol. 47(5), pages 1137-44, September.
  9. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
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Citations

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Cited by:
  1. Joseph M. Ostroy & Uzi Segal, 2010. "No Externalities: A Characterization of Efficiency and Incentive Compatibility with Public Goods," Boston College Working Papers in Economics 769, Boston College Department of Economics.
  2. Murat Sertel, 2000. "Manipulability of the Men-(Women) Optimal Matching Rule via Endowments," Departmental Working Papers, Bilkent University, Department of Economics 0014, Bilkent University, Department of Economics.
  3. Olga Gorelkina, 2014. "Precluding Collusion in the Vickrey Auction," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2014_10, Max Planck Institute for Research on Collective Goods.
  4. Masso, Jordi & Neme, Alejandro, 2007. "Bribe-proof rules in the division problem," Games and Economic Behavior, Elsevier, vol. 61(2), pages 331-343, November.
  5. Mizukami, Hideki & Wakayama, Takuma, 2009. "The relation between non-bossiness and monotonicity," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 256-264, September.
  6. Fujinaka, Yuji & Wakayama, Takuma, 2008. "Secure implementation in economies with indivisible objects and money," Economics Letters, Elsevier, vol. 100(1), pages 91-95, July.
  7. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  8. Sato, Shin, 2013. "A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one," Journal of Economic Theory, Elsevier, vol. 148(1), pages 259-278.
  9. Chen, Jing & Micali, Silvio, 2012. "Collusive dominant-strategy truthfulness," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1300-1312.
  10. Gloria Fiestras-Janeiro & Flip Klijn & Estela S?chez, 2003. "Manipulation of Optimal Matchings via Predonation of Endowment," UFAE and IAE Working Papers 561.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  11. Shigehiro Serizawa, 2006. "Pairwise Strategy-Proofness and Self-Enforcing Manipulation," Social Choice and Welfare, Springer, vol. 26(2), pages 305-331, April.
  12. Peter Eso & James Schummer, 2002. "Bribing and Signalling in Second Price Auctions," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1357, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Juarez, Ruben, 2013. "Group strategyproof cost sharing: The role of indifferences," Games and Economic Behavior, Elsevier, vol. 82(C), pages 218-239.
  14. Ju, Biung-Ghi, 2013. "Coalitional manipulation on networks," Journal of Economic Theory, Elsevier, vol. 148(2), pages 627-662.

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