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Regular version of the site

Book chapter

A-Subgame Concept and the Solutions Properties for Multistage Games with Vector Payoffs

P. 85-102.
Kuzyutin D., Yaroslavna Pankratova, Светлов Р.

We deal with multistage multicriteria games in extensive form and employ so-called “A-subgame” concept to examine dynamical properties of some non-cooperative and cooperative solutions. It is proved that if we take into account only the active players at each A-subgame the set of all strong Pareto equilibria is time consistent but does not satisfy dynamical compatibility.

We construct an optimal cooperative trajectory and vector-valued characteristic function using the refined leximin algorithm. To ensure the sustainability of a cooperative agreement we design the A-incremental imputation distribution procedure for the Shapley value which provides a better incentive for cooperation than classical incremental allocation procedure. This specific payment schedule corresponds to the A-subgame concept satisfies time consistency and efficiency condition and implies non-zero current payment to the active player immediately after her move.

In book

Edited by: L. A. Petrosyan, V. V. Mazalov, N. A. Zenkevich. Birkhäuser, 2019.