Homicidal Chauffeur Game: History and Modern Studies

Patsko, V.S.; Turova, Varvara

doi:10.1007/978-0-8176-8089-3_12

Cited by 14 publications

(11 citation statements)

References 18 publications

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“…We consider a planar system of a pursuer and an evader whose positions, with respect to an inertial Cartesian reference frame, are subject to the following dynamics [18] x…”

Section: A Homicidal-chauffeur Gamementioning

confidence: 99%

“…This is a continuous pursuit-evasion game that can be considered the archetypal of problems of this class and has motivated much research work with early fundamental contribution as in [17]. We refer to [18] for a review of results and a survey of the literature on this topic. We remark that these works focus on a geometrical setting of the HC game and construct solutions based on optimal trajectories and singular lines that disperse, join or refract.…”

Section: Introductionmentioning

confidence: 99%

“…In the HC game formulation, the state of our pursuit-evasion system consists of the planar space coordinates of the position of the players, and the controls/strategies are the velocity of the evader and the radial velocity of turn of the pursuer. As illustrated in [18], we discuss this HC system in an inertial reference frame and in a frame moving with the pursuer. Further, by choosing appropriate values for the weights of the cost functionals, we focus on the case where collision may occur and, correspondingly, determine the time for this event.…”

Section: Introductionmentioning

confidence: 99%

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On the numerical solution of a free end-time homicidal chauffeur game

et al. 2021

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“…We consider a planar system of a pursuer and an evader whose positions, with respect to an inertial Cartesian reference frame, are subject to the following dynamics [18] x…”

Section: A Homicidal-chauffeur Gamementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the numerical solution of a free end-time homicidal chauffeur game

et al. 2021

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“…On the other hand, if v H is much larger than v max and τ min is small, then a E i that finds itself close to H j has no hope of escaping. What might perhaps not be obvious is that even this simple hunter/evader dynamics, known under the name "homicidal chauffeur problem" generates a rich solution space that gives rise to multiple different strategies, depending on the initial conditions and parameters [20]. The rescue scenario now unfolds in the following way: Each hunter H j chooses a route ρ κ to guard and each evader E i chooses a route ρ µ to take.…”

Section: A Game-based Reconciliationmentioning

confidence: 99%

Reconciling White-Box and Black-Box Perspectives on Behavioral Self-adaptation

Bruni

Corradini

Gadducci

et al. 2015

Software Engineering for Collective Autonomic Systems

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Abstract. This paper propose to reconcile two perspectives on behavioural adaptation commonly taken at different stages of the engineering of autonomic computing systems. Requirements engineering activities often take a black-box perspective: A system is considered to be adaptive with respect to an environment whenever the system is able to satisfy its goals irrespectively of the environment disturbations. Modelling and programming engineering activities often take a white-box perspective: A system is equipped with suitable adaptation mechanisms and its behaviour is classified as adaptive depending on whether the adaptation mechanisms are enacted or not. The proposed approach reconciles black-and white-box perspectives by proposing several notions of coherence between the adaptivity as observed by the two perspectives: These notions provide useful criteria for the system developer to assess and possibly modify the adaptation requirements, models and programs of an autonomic system.

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“…For zerosum games, [29] studied a certain Hamiltonian flow which can be used to study the best response dynamic in two-person games, and showed that under certain assumptions the level sets of the associated Hamiltonian function are topological spheres. Further examples of the study of the level sets of the payoff functions for specific games include [18], [24], [25], and [27]. Investigating connections between real algebraic geometry and game theory led to Neyman's work including [23].…”

Section: Bibliographical Notementioning

confidence: 99%

The Level Sets of Typical Games

Rowlett

2014

Notices Amer. Math. Soc.

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In a non-cooperative game, players do not communicate with each other. Their only feedback is the payoff they receive resulting from the strategies they execute. It is important to note that within each level set of the total payoff function the payoff to each player is unchanging, and therefore understanding the structure of these level sets plays a key role in understanding non-cooperative games. This note, intended for both experts and non-experts, not only introduces non-cooperative game theory but also shows its fundamental connection to real algebraic geometry. We prove here a general result about the structure of the level sets, which although likely to be known by experts, has interesting implications, including our recent application to provide a new mathematical explanation for the "paradox of the plankton." We hope to encourage communication between these interrelated areas and stimulate further work in similar directions.

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Homicidal Chauffeur Game: History and Modern Studies

Cited by 14 publications

References 18 publications

On the numerical solution of a free end-time homicidal chauffeur game

On the numerical solution of a free end-time homicidal chauffeur game

Reconciling White-Box and Black-Box Perspectives on Behavioral Self-adaptation

The Level Sets of Typical Games

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