Polynomial calculation of the Shapley value based on sampling

Authors:
Javier Castro;Daniel Gómez;Juan Tejada
Affiliations:
Dpto. de Estadística e I.O. III, Escuela Universitaria de Estadística, Universidad Complutense de Madrid, Av. Puerta de Hierro s/n, 28040 Madrid, Spain;Dpto. de Estadística e I.O. III, Escuela Universitaria de Estadística, Universidad Complutense de Madrid, Av. Puerta de Hierro s/n, 28040 Madrid, Spain;Dpto. de Estadística e I.O. I, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain
Venue:
Computers and Operations Research
Year:
2009

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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.