An Analytic and Numerical Investigation of a Differential Game

Gibali, Aviv; Kelis, Oleg

doi:10.3390/axioms10020066

Cited by 3 publications

(1 citation statement)

References 32 publications

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“…In general, linear-quadratic DGs are analytically and numerically solvable, which can find a variety of applications in reality, such as pursuitevasion problem [185], [186]. Recently, singular linearquadratic DGs were studied in [187], which cannot be handled either using the Isaacs MinMax principle or the Bellman-Isaacs equation approach, and to solve this problem, an interception differential game was introduced with appropriate regularized cost functional and dual representation. The authors in [188] studied a linear-quadratic-Gaussian asset defending differential game where the state information of the attacker and the defender is not accessible to each other, but the trajectory of a moving asset is known by them.…”

Section: Zero-sum Differential Gamesmentioning

confidence: 99%

A Survey of Decision Making in Adversarial Games

Li¹,

Mao²,

Ye³

et al. 2022

Preprint

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Game theory has by now found numerous applications in various fields, including economics, industry, jurisprudence, and artificial intelligence, where each player only cares about its own interest in a noncooperative or cooperative manner, but without obvious malice to other players. However, in many practical applications, such as poker, chess, evader pursuing, drug interdiction, coast guard, cyber-security, and national defense, players often have apparently adversarial stances, that is, selfish actions of each player inevitably or intentionally inflict loss or wreak havoc on other players. Along this line, this paper provides a systematic survey on three main game models widely employed in adversarial games, i.e., zero-sum normal-form and extensive-form games, Stackelberg (security) games, zero-sum differential games, from an array of perspectives, including basic knowledge of game models, (approximate) equilibrium concepts, problem classifications, research frontiers, (approximate) optimal strategy seeking techniques, prevailing algorithms, and practical applications. Finally, promising future research directions are also discussed for relevant adversarial games.

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Section: Zero-sum Differential Gamesmentioning

confidence: 99%

A Survey of Decision Making in Adversarial Games

Li¹,

Mao²,

Ye³

et al. 2022

Preprint

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A survey of decision making in adversarial games

Li,

Meng,

Hong

et al. 2024

Sci. China Inf. Sci.

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Nash Equilibrium Sequence in a Singular Two-Person Linear-Quadratic Differential Game

Glizer

2021

Axioms

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A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the game is linear. Each of the players has a quadratic functional on its own disposal, which should be minimized. The case where weight matrices in control costs of one player are singular in both functionals is studied. Hence, the game under the consideration is singular. A novel definition of the Nash equilibrium in this game (a Nash equilibrium sequence) is proposed. The game is solved by application of the regularization method. This method yields a new differential game, which is a regular Nash equilibrium game. Moreover, the new game is a partial cheap control game. An asymptotic analysis of this game is carried out. Based on this analysis, the Nash equilibrium sequence of the pairs of the players’ state-feedback controls in the singular game is constructed. The expressions for the optimal values of the functionals in the singular game are obtained. Illustrative examples are presented.

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An Analytic and Numerical Investigation of a Differential Game

Cited by 3 publications

References 32 publications

A Survey of Decision Making in Adversarial Games

A Survey of Decision Making in Adversarial Games

A survey of decision making in adversarial games

Nash Equilibrium Sequence in a Singular Two-Person Linear-Quadratic Differential Game

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