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A stochastic approach to approximate values in cooperative games

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  • Benati, Stefano
  • López-Blázquez, Fernando
  • Puerto, Justo

Abstract

Computing additive values in cooperative games, like the Shapley value, is a hard task because, in general, it involves the summation of an exponential number of terms. We propose a new method, based on the stochastic approximation of deterministic games and sampling theory, to calculate a statistic estimate of these values and, at the same time, keeping under control estimation errors. We applied this technique to several well-known games and we show that in many cases we were able to improve previous results.

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  • Benati, Stefano & López-Blázquez, Fernando & Puerto, Justo, 2019. "A stochastic approach to approximate values in cooperative games," European Journal of Operational Research, Elsevier, vol. 279(1), pages 93-106.
    • Handle: RePEc:eee:ejores:v:279:y:2019:i:1:p:93-106
    DOI: 10.1016/j.ejor.2019.05.027
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    2. J. C. Gonçalves-Dosantos & I. García-Jurado & J. Costa & J. M. Alonso-Meijide, 2022. "Necessary players and values," Annals of Operations Research, Springer, vol. 318(2), pages 935-961, November.
    3. A. Saavedra-Nieves & M. G. Fiestras-Janeiro, 2021. "Sampling methods to estimate the Banzhaf–Owen value," Annals of Operations Research, Springer, vol. 301(1), pages 199-223, June.
    4. Saavedra-Nieves, Alejandro & Saavedra-Nieves, Paula, 2020. "On systems of quotas from bankruptcy perspective: the sampling estimation of the random arrival rule," European Journal of Operational Research, Elsevier, vol. 285(2), pages 655-669.
    5. A. Saavedra-Nieves, 2023. "On stratified sampling for estimating coalitional values," Annals of Operations Research, Springer, vol. 320(1), pages 325-353, January.
    6. Luo, Chunlin & Zhou, Xiaoyang & Lev, Benjamin, 2022. "Core, shapley value, nucleolus and nash bargaining solution: A Survey of recent developments and applications in operations management," Omega, Elsevier, vol. 110(C).
    7. Margaretha Gansterer & Richard F. Hartl, 2020. "Shared resources in collaborative vehicle routing," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 1-20, April.

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