A Differential Game with Random Time Horizon and Discontinuous Distribution

Anastasiia Zaremba, Ekaterina Gromova and Anna Tur
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Anastasiia Zaremba: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St Petersburg, Russia
Ekaterina Gromova: Department of Mathematics, St. Petersburg School of Physics, Mathematics, and Computer Science, National Research University Higher School of Economics (HSE), Soyuza Pechatnikov ul. 16, 190008 St. Petersburg, Russia
Anna Tur: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St Petersburg, Russia

Mathematics, 2020, vol. 8, issue 12, 1-21

Abstract: One class of differential games with random duration is considered. It is assumed that the duration of the game is a random variable with values from a given finite interval. The cumulative distribution function (CDF) of this random variable is assumed to be discontinuous with two jumps on the interval. It follows that the player’s payoff takes the form of the sum of integrals with different but adjoint time intervals. In addition, the first interval corresponds to the zero probability of the game to be finished, which results in terminal payoff on this interval. The method of construction optimal solution for the cooperative scenario of such games is proposed. The results are illustrated by the example of differential game of investment in the public stock of knowledge.

Keywords: differential game; random time horizon; discontinuous cdf; dynamic programming principle; open-loop strategies; optimal investment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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