# A Game-Theoretic Model of Pollution Control with Asymmetric Time Horizons

Ekaterina V. Gromova, Anna V. Tur, Lidiya I. Balandina

Research output

### Abstract

In the contribution a problem of pollution control is studied within the game-theoretic framework (Kostyunin et al., 2013; Gromova and Plekhanova, 2015; Shevkoplyas and Kostyunin, 2011). Each player is assumed to have certain equipment whose functioning is related to pollution control. The i-th player’s equipment may undergo an abrupt failure at time Ti. The game lasts until any of the players’ equipment breaks down. Thus, the game duration is defined as T = min(T1, . . . , Tn), where Ti is the time instant at which the i-th player stops the game. We assume that the time instant of the i-th equipment failure is described by the Weibull distribution. According to Weibull distribution form parameter, we consider different scenarios of equipment exploitation, where each of player can be in “an infant”, “an adult” or “an aged” stage. The cooperative 2-player game with different scenarios is studied.
Original language Undefined 170-179 Contributions to Game Theory and Management 9 Published - 2016

### Cite this

@article{9ca715a34af948d4aa764cbd9690b376,
title = "A Game-Theoretic Model of Pollution Control with Asymmetric Time Horizons",
abstract = "In the contribution a problem of pollution control is studied within the game-theoretic framework (Kostyunin et al., 2013; Gromova and Plekhanova, 2015; Shevkoplyas and Kostyunin, 2011). Each player is assumed to have certain equipment whose functioning is related to pollution control. The i-th player’s equipment may undergo an abrupt failure at time Ti. The game lasts until any of the players’ equipment breaks down. Thus, the game duration is defined as T = min(T1, . . . , Tn), where Ti is the time instant at which the i-th player stops the game. We assume that the time instant of the i-th equipment failure is described by the Weibull distribution. According to Weibull distribution form parameter, we consider different scenarios of equipment exploitation, where each of player can be in “an infant”, “an adult” or “an aged” stage. The cooperative 2-player game with different scenarios is studied.",
keywords = "differential game, cooperative game, pollution control, random duration, Weibull distribution",
author = "Gromova, {Ekaterina V.} and Tur, {Anna V.} and Balandina, {Lidiya I.}",
year = "2016",
language = "не определен",
volume = "9",
pages = "170--179",
journal = "Contributions to Game Theory and Management",
issn = "2310-2608",

}

In: Contributions to Game Theory and Management, Vol. 9, 2016, p. 170-179.

Research output

TY - JOUR

T1 - A Game-Theoretic Model of Pollution Control with Asymmetric Time Horizons

AU - Gromova, Ekaterina V.

AU - Tur, Anna V.

AU - Balandina, Lidiya I.

PY - 2016

Y1 - 2016

N2 - In the contribution a problem of pollution control is studied within the game-theoretic framework (Kostyunin et al., 2013; Gromova and Plekhanova, 2015; Shevkoplyas and Kostyunin, 2011). Each player is assumed to have certain equipment whose functioning is related to pollution control. The i-th player’s equipment may undergo an abrupt failure at time Ti. The game lasts until any of the players’ equipment breaks down. Thus, the game duration is defined as T = min(T1, . . . , Tn), where Ti is the time instant at which the i-th player stops the game. We assume that the time instant of the i-th equipment failure is described by the Weibull distribution. According to Weibull distribution form parameter, we consider different scenarios of equipment exploitation, where each of player can be in “an infant”, “an adult” or “an aged” stage. The cooperative 2-player game with different scenarios is studied.

AB - In the contribution a problem of pollution control is studied within the game-theoretic framework (Kostyunin et al., 2013; Gromova and Plekhanova, 2015; Shevkoplyas and Kostyunin, 2011). Each player is assumed to have certain equipment whose functioning is related to pollution control. The i-th player’s equipment may undergo an abrupt failure at time Ti. The game lasts until any of the players’ equipment breaks down. Thus, the game duration is defined as T = min(T1, . . . , Tn), where Ti is the time instant at which the i-th player stops the game. We assume that the time instant of the i-th equipment failure is described by the Weibull distribution. According to Weibull distribution form parameter, we consider different scenarios of equipment exploitation, where each of player can be in “an infant”, “an adult” or “an aged” stage. The cooperative 2-player game with different scenarios is studied.

KW - differential game

KW - cooperative game

KW - pollution control

KW - random duration

KW - Weibull distribution

M3 - статья

VL - 9

SP - 170

EP - 179

JO - Contributions to Game Theory and Management

JF - Contributions to Game Theory and Management

SN - 2310-2608

ER -