On the form of integral payoff in differential games with random duration

Gromova, Ekaterina; Tur, Anna

doi:10.1109/icat.2017.8171597

Cited by 2 publications

(4 citation statements)

References 14 publications

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“…Optimal trajectory on the first interval (10) under assumption of p 1 and p 2 aiming to 0 also gives the results (16):…”

Section: Assumption Of No Jumps In Cdfmentioning

confidence: 78%

“…The payoff on the other intervals is nothing but a mathematical expectation of the integration payoff corresponding to the particular form of the CDF on the interval. Thus, accordingly to (5) and proof in [10], the total payoff of the player could be written as the sum of four adjoint integrals (6).…”

Section: Problem Formulationmentioning

confidence: 99%

“…It is assumed that the duration of the game is a random variable corresponding to the discontinuous cumulative distribution function (CDF). Particular classes of discontinuous models had been formulated in [9] for the case with only one jump and in [10] for the step form of the CDF. In this paper, the discontinuous structure of the CDF of the game implies that the game can not be interrupted until a certain point, then could stop either on the continuous interval or in the certain discrete-time moments.…”

Section: Introductionmentioning

confidence: 99%

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A Differential Game with Random Time Horizon and Discontinuous Distribution

2020

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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.

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“…Optimal trajectory on the first interval (10) under assumption of p 1 and p 2 aiming to 0 also gives the results (16):…”

Section: Assumption Of No Jumps In Cdfmentioning

confidence: 78%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Differential Game with Random Time Horizon and Discontinuous Distribution

2020

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“…The transformation of integral functional in the form of double integral (Equation (3)) to the standard for dynamic programming form is important for further study of the game (see also [26]). 3has the following form:…”

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confidence: 99%

Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration

2018

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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.

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On the form of integral payoff in differential games with random duration

Cited by 2 publications

References 14 publications

A Differential Game with Random Time Horizon and Discontinuous Distribution

A Differential Game with Random Time Horizon and Discontinuous Distribution

Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration

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