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Keywords = discontinuous cdf

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21 pages, 449 KB  
Article
A Differential Game with Random Time Horizon and Discontinuous Distribution
by Anastasiia Zaremba, Ekaterina Gromova and Anna Tur
Mathematics 2020, 8(12), 2185; https://doi.org/10.3390/math8122185 - 8 Dec 2020
Cited by 6 | Viewed by 2417
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Statistical and Probabilistic Methods in the Game Theory)
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17 pages, 363 KB  
Article
Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration
by Ekaterina Gromova, Anastasiya Malakhova and Arsen Palestini
Mathematics 2018, 6(9), 165; https://doi.org/10.3390/math6090165 - 11 Sep 2018
Cited by 9 | Viewed by 3684
Abstract
A nonrenewable resource extraction game model is analyzed in a differential game theory framework with random duration. If the cumulative distribution function (c.d.f.) of the final time is discontinuous, the related subgames are differentiated based on the position of the initial instant with [...] Read more.
A nonrenewable resource extraction game model is analyzed in a differential game theory framework with random duration. If the cumulative distribution function (c.d.f.) of the final time is discontinuous, the related subgames are differentiated based on the position of the initial instant with respect to the jump. We investigate properties of optimal trajectories and of imputation distribution procedures if the game is played cooperatively. Full article
(This article belongs to the Special Issue Mathematical Game Theory)
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