Pré-Publication, Document De Travail Année : 2025

Approximating the Shapley value with sampling : survey and new stratification techniques

Résumé

In game theory, a cooperative game can be used to model a system able to provide a service to a set of users for a certain cost. An important topic related to cooperative games is the cost sharing which distributes the total cost of the system among the players. Shapley proposed in 1953 a cost-sharing mechanism nowadays known as the Shapley value. It is usually interpreted as assigning to each player the cost this player induces on the system. This cost assignment has many desirable properties but it is very time consuming to compute exactly when the number of users is large. Thus, a large effort has been directed towards its approximation. Many general purpose algorithms for computing the Shapley value use sampling, and in particular stratified sampling, in order to obtain a good approximation. In this paper, we provide a comprehensive overview for approximating the Shapley value with sampling with a focus on how and why stratified sampling helps enhancing the precision of the approximation. We also propose a new paradigm to apply stratification which is more flexible than the currently used schemes and allows one to adjust the stratification decisions to the result of the sampling process. We suggest a methodology to create datasets containing a large number of random games to test Shapley approximation algorithms. Finally, we report an extensive experimental study of all the algorithms described in the paper on the datasets created using the previous methodology.

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hal-04995993 , version 1 (18-03-2025)

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  • HAL Id : hal-04995993 , version 1

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François Lamothe, Sandra Ulrich Ngueveu. Approximating the Shapley value with sampling : survey and new stratification techniques. 2025. ⟨hal-04995993⟩
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