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The idea of approximating the Shapley value of an n-person game by Monte Carlo simulation was first suggested by Mann and Shapley (1960) and they also introduced four different heuristical methods to reduce the estimation error.
A value for n-person games
Shapley, L. S. 1953 · 1953
Earlier work this paper cites.
Values of large games, IV: Evaluating the electoral college by Montecarlo techniques
Mann, I., and L. S. Shapley. 1960 · 1960
Earlier work this paper cites.
Multilinear extensions of games
Owen, G. 1972 · 1972
Earlier work this paper cites.
Computational complexity of the game theory approach to cost allocation for a tree
Megiddo, N. 1978 · 1978
Earlier work this paper cites.
Cooperative games, solutions and applications , vol. 3
Driessen, T. S. 1988 · 1988
Earlier work this paper cites.
The Shapley value for cooperative games under precedence constraints
Faigle, U., and W. Kern. 1992 · 1992
Earlier work this paper cites.
On the complexity of cooperative solution concepts
Deng, X., and C. H. Papadimitriou. 1994 · 1994
Cited alongside, same era.
Cost allocation for a tree network with heterogeneous customers
Granot, D., J. Kuipers, and S. Chopra. 2002 · 2002
Cited alongside, same era.
Computing power indices for large voting games
Leech, D. 2003 · 2003
Cited alongside, same era.
A polynomial rule for the problem of sharing delay costs in PERT networks
Castro, J., D. Gómez, and J. Tejada. 2008 · 2006
Cited alongside, same era.
Polynomial calculation of the Shapley value based on sampling
———. 2009 · 2008
Cited alongside, same era.
Bounding the estimation error of sampling-based Shapley value approximation with/without stratifying
Maleki, S., L. Tran-Thanh, G. Hines, T. Rahwan, and A. Rogers. 2013 · 2013
Cited alongside, same era.
Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update
Thomson, W. 2015 · 2015
Later among the works it cites.
Improving polynomial estimation of the Shapley value by stratified random sampling with optimum allocation
Castro, J., D. Gómez, E. Molina, and J. Tejada. 2017 · 2017
Later among the works it cites.
Liability games
Csóka, P., and P. J.-J. Herings. 2019 · 2019
Closest in time.
A Bayesian Monte Carlo method for computing the Shapley value: Application to weighted voting and bin packing games
Touati, S., M. S. Radjef, and S. Lakhdar. 2021 · 2020
Closest in time.
On the Shapley value of liability games
Csóka, P., F. Illés, and T. Solymosi. 2022 · 2021
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