In the paper the evolution of dynamic game along the cooperative trajectory is investigated. Along cooperative trajectory at each time instant players find themselves in a new game which is a subgame of the originally defined game. In many cases the optimal solution of the initial game restricted to the subgame along cooperative trajectory fails to be optimal in the subgame. To overcome this difficulty we introduced (see Petrosyan and Danilov, Vestnik Leningrad Univ Mat Mekh Astronom 1:52–59, 1979; Petrosyan and Zaccour, J Econ Control 27(3):381–398, 2003; Yeung and Petrosyan, Subgame consistent economic optimization. Birkhauser, 2012) the special payment mechanism—imputation distribution procedure (IDP), or payment distribution procedure (PDP), but another serious question arises: under what conditions the initial optimal solution converted to any optimal solution in the subgame will remain optimal in the whole game. This condition we call strongly time-consistency condition of the optimal solution. If this condition is not satisfied players in reality may switch in some time instant from the previously selected optimal solution to any optimal solution in the subgame, and as result realize the solution which will be not optimal in the whole game. We propose different types of strongly time-consistent solutions for multicriterial control, cooperative differential, and cooperative dynamic games.

Original languageEnglish
Title of host publicationFrontiers in Games and Dynamic Games
Subtitle of host publicationAnnals of the International Society of Dynamic Games
PublisherBirkhäuser Verlag AG
Pages23-37
Number of pages15
Volume16
ISBN (Electronic)978-3-030-39789-0
ISBN (Print)978-3-030-39788-3
DOIs
StatePublished - 2020

Publication series

NameAnnals of the International Society of Dynamic Games
Volume16
ISSN (Print)2474-0179
ISSN (Electronic)2474-0187

    Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

    Research areas

  • Cooperation, Differential game, Dynamic stability, Pareto optimality, Time consistency

ID: 61121012