The Shapley Value as a Sustainable Cooperative Solution in Differential Games of Three Players

  • Ekaterina GromovaEmail author
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)


The contribution of the paper is twofold: first, it has been shown that the Yeung’s conditions can be used to construct a strongly time-consistent core. In this core there is a supporting imputation which has the property that a single deviation from this imputation in favor of any other imputation from the core still leads to the payment from the core. The obtained results were formulated for the Shapley value taken as the supporting imputation. Second, a particular class of differential games was considered. For this class of games the δ-characteristic function turns out to be superadditive and the Yeung’s conditions are satisfied without any additional restrictions on the parameters of the model. All results are presented in the analytic form.


Shapley value Core Cooperative game Differential game Pollution control Time-consistency Strong time-consistency Irrational behavior proofness 



The author acknowledges the grants, 9.41.723.2015, and 9.42.1043.2016 from St. Petersburg State University. A part of this research was conducted while visiting prof. G. Zaccour at GERAD, Montreal, Canada, February 2015.

The author is grateful to the anonymous reviewers for the valuable comments.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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