Abstract
The problem of strategically provided cooperation in m-person differential games for a prescribed duration and integral payoffs is considered. The Shapley value operator is chosen as the cooperative optimality principle. It is shown that components of Shapley value are absolutely continuous and, thus, differentiable functions along any admissible trajectory. The main result consists in the fact that if in any subgame along the cooperative trajectory the Shapley value belongs to the core of this subgame, then the payoffs as components of the Shapley value can be realized in a specially constructed strong Nash equilibrium, i.e., an equilibrium that is stable against the deviation of coalitions.
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Chistyakov, S., Petrosyan, L. (2013). Strong Strategic Support of Cooperative Solutions in Differential Games. In: Cardaliaguet, P., Cressman, R. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8355-9_5
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DOI: https://doi.org/10.1007/978-0-8176-8355-9_5
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