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Contributions to Game Theory and Management, 2020, Volume 13, Pages 360–387 (Mi cgtm375)  

Looking forward approach with random horizon in cooperative differential games

Ovanes Petrosianab, Sergei Pogozheva

a St. Petersburg State University, Faculty of Applied Mathematics and Control Processes, Universitetskaya emb. 7/9, St.Petersburg, 198504, Russia
b National Research University Higher School of Economics, 3A Kantemirovskaya Street, Saint Petersburg, Russia

Abstract: In the paper authors present a new approach to determination and computation of a solution for differential games with prescribed duration in the case when players lack certain information about the dynamical system and payoff function on the whole time interval on which the game is played. At each time instant players receive information about dynamical system and payoff functions, however the duration of the period of this information is unknown and can be represented as a random variable with known parameters. At certain periods of time the information is updated. A novel solution is described as a combination of imputation sets in the truncated subgames that are analyzed using Looking Forward Approach with random horizon. A resource extraction game serves as an illustration in order to compare a cooperative trajectory, imputations, and imputation distribution procedure in the game with Looking Forward Approach and in the original game with prescribed duration. Looking Forward Approach is used for constructing game theoretical models and defining solutions for conflict-controlled processes where information about the process updates dynamically.

Keywords: differential games, time-consistency, predictive control.

Funding Agency Grant Number
Russian Science Foundation 18-71-00081
The research of first author was supported by a grant from the Russian Science Foundation (Project No 18-71-00081).


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Citation: Ovanes Petrosian, Sergei Pogozhev, “Looking forward approach with random horizon in cooperative differential games”, Contributions to Game Theory and Management, 13 (2020), 360–387

Citation in format AMSBIB
\Bibitem{PetPog20}
\by Ovanes~Petrosian, Sergei~Pogozhev
\paper Looking forward approach with random horizon in cooperative differential games
\jour Contributions to Game Theory and Management
\yr 2020
\vol 13
\pages 360--387
\mathnet{http://mi.mathnet.ru/cgtm375}


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