Complutense University Library

Polynomial calculation of the Shapley value based on sampling

Castro, Javier and Gómez, Daniel and Tejada Cazorla, Juan Antonio (2009) Polynomial calculation of the Shapley value based on sampling. Computers and Operations Research, 36 (5). pp. 1726-1730. ISSN 0305-0548

[img] PDF
Restricted to Repository staff only until 2020.

159kB

Official URL: http://www.sciencedirect.com/science/article/pii/S0305054808000804

View download statistics for this eprint

==>>> Export to other formats

Abstract

In this paper we develop a polynomial method based on sampling theory that can be used to estimate the Shapley value (or any semivalue) for cooperative games. Besides analyzing the complexity problem, we examine some desirable statistical properties of the proposed approach and provide some computational results.


Item Type:Article
Uncontrolled Keywords:Game theory; Shapley value; Sampling algorithm
Subjects:Sciences > Mathematics > Operations research
ID Code:15904
References:

Shapley LS. A value for n-person games. In: Kuhn HW, Tucker AW, editors. Contributions to the theory of games II, Annals of mathematics studies, vol.28. Princeton, NJ: Princeton University Press; 1957. p. 307--17.

Deng X, Papadimitriou CH. On the complexity of cooperative solution concepts.Mathematics of Operations Research 1994;19(2):257--66.

Fernández JR, Algaba E, Bilbao JM, Jim´enez A, Jiménez N, López JJ. Generating functions for computing the Myerson value. Annals of Operations Research 2002;109:143--58.

Faigle U, Kern W. The Shapley value for cooperative games under precedence constraints. International Journal of Game Theory 1992;21(3):249--66.

Bilbao JM, Fernández JR, Jiménez Losada A, López JJ. Generating functions for computing power indices efficiently. TOP 2000;8(2):191--213.

Granot D, Kuipers J, Chopra S. Cost allocation for a tree network with heterogeneous customers. Mathematics of Operations Research 2002;27(4):647--61.

Castro J, G´omez D, Tejada J. A polynomial rule for the problem of sharing delay costs in PERT networks. Computers and Operation Research 2008;35(7):2376--87.

Owen G. Multilinear extensions of games. Management Science Series B---Application 1972;18(5):64--79.

Fatima SS, Wooldridge M, Jenniggs NR. An analysis of the Shapley value and its uncertainty for the voting game. Lectures notes in artificial intelligence, vol.3937, 2006. p. 85--98.

Cochran WG. Sampling techniques. New York: Wiley; 1977.

Lohr H. Sampling: design and analysis. Duxbury; 1999.

Dubey P, Neyman A, Weber RJ. Value theory without efficiency. Mathematics of Operations Research 1981;6(1):122--8.

Owen G. Game theory. New York: Academic Press; 1995.

Deposited On:11 Jul 2012 10:31
Last Modified:06 Feb 2014 10:34

Repository Staff Only: item control page