Strongly Time-Consistent Core  in Differential Games with Discrete Distribution of Random Time Horizon

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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“…This game formulation of differential game with discrete random time horizon was investigated in [22]. Consider cooperative form of the game:…”

Section: Assumption Of a Piece-wise Constant Cdfmentioning

confidence: 99%

A Differential Game with Random Time Horizon and Discontinuous Distribution

2020

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“…In [20], a random time horizon hybrid (see also [21] for a general treatment of hybrid differential games) differential game was considered such that the probability distribution can change over time. Differential games with discrete random variable of time horizon and corresponding time-consistency problem were considered recently in [22]. Time-consistency notation for multistage games with vector payoffs was introduced in [23].…”

Section: Introductionmentioning

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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Strongly Time-Consistent Core in Differential Games with Discrete Distribution of Random Time Horizon

Cited by 2 publications

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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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