A Note on the Number of alpha-Pivotal Players

作者：Becker Johannes Gerd^*

来源：Mathematics of Operations Research, 2012, 37(1): 196-200.

DOI：10.1287/moor.1110.0523

• alpha-pivotal agent
• influence
• direct mechanism
• decomposition of variance

We show that bounds like those of Al-Najjar and Smorodinsky [Al-Najjar, N. I., R. Smorodinsky. 2000. Pivotal players and the characterization of influence. J. Econom. Theory 92(2) 318-342] as well as of Gradwohl et al. [Gradwohl, R., O. Reingold, A. Yadin, A. Yehudayoff. 2009. Players' effects under limited independence. Math. Oper. Res. 34(4) 971-980] on the number of alpha-pivotal agents, derived by a combinatorial approach, can be obtained by decomposition of variance, i.e., an orthogonality argument as used in Appendix 1 of Mailath and Postlewaite [Mailath, G. J., A. Postlewaite. 1990. Asymmetric information bargaining problems with many agents. Rev. Econom. Stud. 57(3) 351-367]. All these bounds have a similar asymptotic behavior, up to constant factors. Our bound is weaker than that of Al-Najjar and Smorodinsky, but we require only pairwise independent-rather than independent-types. Our result strengthens the bound of Gradwohl et al.

• 出版日期2012-2