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Secure implementation in allotment economies

  • Bochet, Olivier
  • Sakai, Toyotaka

An allocation rule is securely implementable if it is strategy-proof and has no "bad" Nash equilibrium in its associated direct revelation game [Saijo, T., Sjöström, T., Yamato, T., 2007. Secure implementation. Theoretical Econ. 2, 203-229. Original work published in RIETI Discussion Paper (03-E-019), 2003]. We study this implementability notion in allotment economies with single-peaked preferences [Sprumont, Y., 1991. The division problem with single-peaked preferences: A characterization of the uniform allocation rule. Econometrica 59, 509-519]. The equal division rule and priority rules are characterized on the basis of secure implementability, which underlines a strong trade-off between efficiency and symmetry. Though the uniform rule is not securely implementable, we show that, in its direct revelation game, any "bad" Nash equilibrium is blocked by a credible coalitional deviation, and any "good" Nash equilibrium is never blocked. Thus the impossibility of securely implementing the uniform rule can be resolved by allowing pre-play communication among players.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 68 (2010)
Issue (Month): 1 (January)
Pages: 35-49

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Handle: RePEc:eee:gamebe:v:68:y:2010:i:1:p:35-49
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  1. Moulin, Herv�, 1998. "Rationing a Commodity Along Fixed Paths," Working Papers 98-01, Duke University, Department of Economics.
  2. Yuji Fujinaka & Takuma Wakayama, 2007. "Secure Implementation in Economies with Indivisible Objects and Money," ISER Discussion Paper 0699, Institute of Social and Economic Research, Osaka University.
  3. Timothy N. Cason & Tatsuyoshi Saijo & Tomas Sjostrom & Takehiko Yamato, 2005. "Secure Implementation Experiments: Do Strategy-proof Mechanisms Really Work?," Economics Working Papers 0055, Institute for Advanced Study, School of Social Science.
  4. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  5. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1999. "On Coalition-Proof Nash Equilibria in Common Agency Games," Journal of Economic Theory, Elsevier, vol. 85(1), pages 122-139, March.
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  7. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
  8. Tatsuyoshi Saijo & Tomas Sjöström & Takehiko Yamato, 2004. "Secure Implementation," Levine's Bibliography 122247000000000615, UCLA Department of Economics.
  9. Shigehiro Serizawa, 2006. "Pairwise Strategy-Proofness and Self-Enforcing Manipulation," Social Choice and Welfare, Springer, vol. 26(2), pages 305-331, April.
  10. Yuji Fujinaka & Takuma Wakayama, 2011. "Secure implementation in Shapley–Scarf housing markets," Economic Theory, Springer, vol. 48(1), pages 147-169, September.
  11. Lars Ehlers, 2002. "Resource-monotonic allocation when preferences are single-peaked," Economic Theory, Springer, vol. 20(1), pages 113-131.
  12. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
  13. Shinohara, Ryusuke, 2005. "Coalition-proofness and dominance relations," Economics Letters, Elsevier, vol. 89(2), pages 174-179, November.
  14. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
  15. Yi, Sang-Seung, 1999. "On the Coalition-Proofness of the Pareto Frontier of the Set of Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 26(2), pages 353-364, January.
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