TY - CHAP

T1 - Strongly Time-Consistent Solutions in Cooperative Dynamic Games

AU - Петросян, Леон Аганесович

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2020.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Cooperation

KW - Differential game

KW - Dynamic stability

KW - Pareto optimality

KW - Time consistency

UR - http://www.scopus.com/inward/record.url?scp=85090732884&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/ee130d7f-aa25-3622-8183-d5dde152a670/

U2 - 10.1007/978-3-030-39789-0_2

DO - 10.1007/978-3-030-39789-0_2

M3 - Chapter

SN - 978-3-030-39788-3

VL - 16

T3 - Annals of the International Society of Dynamic Games

SP - 23

EP - 37

BT - Frontiers in Games and Dynamic Games

PB - Birkhäuser Verlag AG

ER -