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

  • Denis KuzyutinEmail author
  • Yaroslavna Pankratova
  • Roman Svetlov
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)


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.


Dynamic game Multiple criteria decision making Multicriteria game Shapley value Cooperative solution Time consistency Pareto equilibria 



The research of the first and the second author was funded by RFBR under the research project 18-00-00727 (18-00-00725). The research of the third author was funded by RFBR under the research project 18-00-00727 (18-00-00628).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Denis Kuzyutin
    • 1
    • 2
    Email author
  • Yaroslavna Pankratova
    • 1
  • Roman Svetlov
    • 3
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.National Research University Higher School of Economics at St. PetersburgSt. PetersburgRussia
  3. 3.The Herzen State Pedagogical University of RussiaSt. PetersburgRussia

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