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Secure implementation in allotment economies

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  • Bochet, Olivier
  • Sakai, Toyotaka

Abstract

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.

Suggested Citation

  • Bochet, Olivier & Sakai, Toyotaka, 2010. "Secure implementation in allotment economies," Games and Economic Behavior, Elsevier, vol. 68(1), pages 35-49, January.
  • Handle: RePEc:eee:gamebe:v:68:y:2010:i:1:p:35-49
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    References listed on IDEAS

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    1. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
    2. Sjostrom, Tomas & Yamato, Takehiko & Saijo, Tatsuyoshi, 2007. "Secure implementation," Theoretical Economics, Econometric Society, vol. 2(3), September.
    3. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    4. Fujinaka, Yuji & Wakayama, Takuma, 2008. "Secure implementation in economies with indivisible objects and money," Economics Letters, Elsevier, vol. 100(1), pages 91-95, July.
    5. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
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    9. 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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    12. Yuji Fujinaka & Takuma Wakayama, 2011. "Secure implementation in Shapley–Scarf housing markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 147-169, September.
    13. 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.
    14. 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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    Citations

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    Cited by:

    1. Fujinaka, Yuji & Wakayama, Takuma, 2008. "Secure implementation in economies with indivisible objects and money," Economics Letters, Elsevier, vol. 100(1), pages 91-95, July.
    2. Kumar, Rajnish, 2013. "Secure implementation in production economies," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 372-378.
    3. Katsuhiko Nishizaki, 2013. "An impossibility theorem for secure implementation in discrete public good economies," Economics Bulletin, AccessEcon, vol. 33(1), pages 300-308.
    4. Yuji Fujinaka & Takuma Wakayama, 2011. "Secure implementation in Shapley–Scarf housing markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 147-169, September.
    5. Katsuhiko Nishizaki, 2014. "An equivalence of secure implementability and full implementability in truthful strategies in pure exchange economies with Leontief utility functions," Review of Economic Design, Springer;Society for Economic Design, vol. 18(1), pages 73-82, March.
    6. William Thomson, 2010. "Implementation of solutions to the problem of fair division when preferences are single-peaked," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 1-15, March.
    7. Adachi, Tsuyoshi, 2010. "The uniform rule with several commodities: A generalization of Sprumont's characterization," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 952-964, November.
    8. Adachi, Tsuyoshi, 2014. "Robust and secure implementation: equivalence theorems," Games and Economic Behavior, Elsevier, vol. 86(C), pages 96-101.
    9. Hirofumi Yamamura & Ryo Kawasaki, 2013. "Generalized average rules as stable Nash mechanisms to implement generalized median rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 815-832, March.
    10. Toyotaka Sakai & Takuma Wakayama, 2008. "Uniform, Equal Division, and Other Envy-free Rules between the Two," ISER Discussion Paper 0723, Institute of Social and Economic Research, Osaka University.

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