Secure implementation in allotment economies

Olivier Bochet, Toyotaka Sakai

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)35-49
Number of pages15
JournalGames and Economic Behavior
Issue number1
StatePublished - Jan 2010


  • Coalition-proof Nash equilibrium
  • Fair allocation
  • Nash implementation
  • Priority rule
  • Secure implementation
  • Single-peaked preference
  • Strategy-proofness
  • Uniform rule

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics


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