TY - JOUR

T1 - A differential game with random time horizon and discontinuous distribution

AU - Заремба, Анастасия Павловна

AU - Gromova, Ekaterina

AU - Tur, Anna

N1 - Funding Information: Funding: The work by E. Gromova on the formulation and general solution of the problem was supported by the grant from Russian Science Foundation 17-11-01093, while the development of analytical methods used for obtaining the solution performed by A. Tur was supported by RFBR under the research project 18-00-00727 (18-00-00725). Publisher Copyright: © 2020 by the authors. Licensee MDPI, Basel, Switzerland. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/12

Y1 - 2020/12

N2 - 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.

AB - 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.

KW - Differential game

KW - Discontinuous cdf

KW - Dynamic programming principle

KW - Open-loop strategies

KW - Optimal investment

KW - Random time horizon

UR - http://www.scopus.com/inward/record.url?scp=85097520837&partnerID=8YFLogxK

U2 - 10.3390/math8122185

DO - 10.3390/math8122185

M3 - Article

AN - SCOPUS:85097520837

VL - 8

SP - 1

EP - 21

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 12

M1 - 2185

ER -