不完全信息时高考博弈分析

:c,c,.......... 考生i+1—考生N的偏好P321

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:c1,c2,..........,Pi*':c2,c1,..........。这里，省略号表示其他学对于考生i，他的两个偏好Pi*

校的任意排序。

我们有 i*(P,P i*)=c1, i*(Pi*',P i*)≠c1，考生i把学校c1作为第一志愿，在第一论i*

该校有空余名额他可以被录取，但是他把学校c1作为第二志愿时，第二轮他的分数不够高，不会被录取c1录取。 但是即使把学校c2列为第一志愿，他由于分数不是很高，根本不会被学校c2录取

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i(Pi',P i)≠c2。因此，存在考生i*∈S，对于两个偏好

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Pi*:c1,c2,..........,Pi*':c2,c1,..........，存在P i*满足P i*∈T1\S1,P i* S2\T2，使得T1\S1≠S2\T2。

由于μ的性质，考生i的边际偏好分布的支撑集合必然是全部可能的偏好，因此上面的偏好是可能的。在志愿优先的机制下，低分考生可以利用高分考生的偏好“撞车”来得到

比较好的结果，但这也使得真实填报志愿不能构成均衡。因此，对几乎所有信念来说，实话实说不是序数贝叶斯激励相容的。Q.E.D.

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参 考 文 献

[1] Abdulkadiroglu, Atila, Tayfun Sonmez, “School Choice: A Mechanism Design Approach” ,

American Economic Review, 2003, 93(3),729-47

[2] Abdulkadiroglu, Atila , Parag A. Pathak, and Alvin E. Roth, “The New York City High

School Match”, American Economic Review, Papers and Proceedings, 2005, 95,2, 364-367. [3] Abdulkad roglu, Atila; Pathak, Parag A.; Roth, Alvin E.; Sönmez, Tayfun. “The Boston

Public School Match”, American Economic Review, 2005, Vol. 95 Issue 2, p368-371

[4] Abdulkadiroglu, Atila, Parag A. Pathak, Alvin E. Roth, and Tayfun Sonmez, "Changing the

Boston School Choice Mechanism," 2006. NBER Working paper

[5] C.d’Aspremont and B.Peleg，“Ordinal Bayesian Incentive Compatible Representation of

Committees”, Social Choice and Welfare 1988，5, 261-280

[6] Balinski, Michel; Sonmez Tayfun, “A Tale of Two Mechanisms: Student Placement”,

Journal of Economic Theory, 1999, 84(1), pp. 73-94

[7] Chen Yan, Tayfun Sonmez, “School Choice：An Experiment Study”, Journal of Economic

Theory, 2006, 127, 202-231

[8] Lars Ehlers, "In Search of Advice for Physicians in Entry-Level Medical Markets", 2003,

[9] Lars Ehlers, "In search of advice for participants in matching markets which use the

deferred-acceptance algorithm", Games and Economic Behavior, 2004, vol. 48(2), 249-270, [10] L. Ehlers and J. Massó, “Incomplete Information and Small Cores in Matching Market”,