TY - JOUR
T1 - Secure implementation in allotment economies
AU - Bochet, Olivier
AU - Sakai, Toyotaka
N1 - Funding Information:
✩ The authors deeply thank the associate editor, two anonymous referees, Tsuyoshi Adachi, Ryusuke Shinohara and Takuma Wakayama for their helpful advices. This paper was presented at Hitotsubashi Workshop on Choice, Games, and Welfare, the Conference in honor of Professor Jun Iritani’s 60th birthday at Osaka Keizai University, and the CRETA spring workshop 2009 at the University of Warwick. Part of this paper was written when O. Bochet was visiting Yokohama National University, which was supported by KAKENHI (18730132). * Corresponding author. E-mail addresses: [email protected] (O. Bochet), [email protected] (T. Sakai). URLs: http://staff.unibe.ch/bochet (O. Bochet), http://www.geocities.jp/toyotaka_sakai/ (T. Sakai).
PY - 2010/1
Y1 - 2010/1
N2 - 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.
AB - 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.
KW - Coalition-proof Nash equilibrium
KW - Fair allocation
KW - Nash implementation
KW - Priority rule
KW - Secure implementation
KW - Single-peaked preference
KW - Strategy-proofness
KW - Uniform rule
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U2 - 10.1016/j.geb.2009.04.023
DO - 10.1016/j.geb.2009.04.023
M3 - Article
AN - SCOPUS:72049117351
SN - 0899-8256
VL - 68
SP - 35
EP - 49
JO - Games and Economic Behavior
JF - Games and Economic Behavior
IS - 1
ER -