Dynamic Noncooperative Game Theory, 2nd Edition

Başar, Tamer; Olsder, Geert Jan

doi:10.1137/1.9781611971132

Cited by 1,878 publications

(2,630 citation statements)

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“…Let u * p := BR(u * e ). Then, (u * e and u * p ) are called the (open-loop) Stackelberg strategies of this differential game [2].…”

Section: Problem Definitionmentioning

confidence: 99%

“…Pursuit-evasion games have been used for modeling various problems of conflict arising between two dynamic agents with opposing interests [1,2]. Some examples include multiagent collision avoidance [3], air combat [4], and path planning in an adversarial environment [5].…”

Section: Introductionmentioning

confidence: 99%

“…Analytical solutions to certain classes of pursuit-evasion games, e.g., the "homicidal chauffeur" and the "lady in the lake" games, exist [1,2]. However, for problems involving agents with more complex dynamics, or for problems involving complex environments (e.g., including obstacles), existing analytical techniques are difficult to apply.…”

Section: Introductionmentioning

confidence: 99%

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Incremental Sampling-Based Algorithms for a Class of Pursuit-Evasion Games

Karaman

2010

Springer Tracts in Advanced Robotics

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Pursuit-evasion games have been used for modeling various forms of conflict arising between two agents modeled as dynamical systems. Although analytical solutions of some simple pursuit-evasion games are known, most interesting instances can only be solved using numerical methods requiring significant offline computation. In this paper, a novel incremental sampling-based algorithm is presented to compute optimal open-loop solutions for the evader, assuming worst-case behavior for the pursuer. It is shown that the algorithm has probabilistic completeness and soundness guarantees. As opposed to many other numerical methods tailored to solve pursuit-evasion games, incremental sampling-based algorithms offer anytime properties, which allow their real-time implementations in online settings.

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“…Let u * p := BR(u * e ). Then, (u * e and u * p ) are called the (open-loop) Stackelberg strategies of this differential game [2].…”

Section: Problem Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Incremental Sampling-Based Algorithms for a Class of Pursuit-Evasion Games

Karaman

2010

Springer Tracts in Advanced Robotics

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“…This is an N -person stochastic differential game. There are a lot of situations in the area that one can discuss; see [1] for a general exposition. Here, we only consider the so-called non-cooperative differential games, namely, the -th player in the game would like to minimize his/her own cost functional J (u(·), regardless of other players' cost functionals.…”

Section: Proof Let Us Suppress (Tx(t) P(t) Q(t)) For Any V(·)mentioning

confidence: 99%

A Variational Formula for Stochastic Controls and Some Applications

Mou¹,

Yong²

2007

Pure and Applied Mathematics Quarterly

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For a controlled stochastic differential equation with a Bolza type performance functional, a variational formula for the functional in a given control process direction is derived, by means of backward stochastic differential equations. As applications, some Pontryagin type maximum principles are established for optimal controls of control problems, for saddle points of open-loop two-person zero-sum differential games, and for Nash equilibria of N -person nonzero-sum differential games. The results presented in this paper generalizes/simplifies the relevant ones found in [12] [17]. In addition, a sufficient existence condition of Nash equilibria is proved for nonzero-sum games.

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“…Note that ν is a fixed angle (it does not vary with time), whereas α generally does vary with time. With this criterion one enters the realm of dynamic game theory [1]. It is of course possible to relax the bounds on the admissible ν somewhat.…”

Section: Other Variationsmentioning

confidence: 99%

Bicycle Routing for Maximum Suntan

Olsder

2003

SIAM Rev.

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Abstract.A simple optimal control problem is formulated in which one must find the optimal path along which to bike in order to get maximum suntan. Both the maximum principle and the Euler equation of the classical calculus of variations are used to calculate this optimal path. The interrelationship of the two approaches is elucidated; the adjoint variables in the maximum principle approach (which happen to be constants) are integration constants when solving via the Euler equation. Several slightly different versions of this problem are treated, with some surprising phenomena in the solution.

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Dynamic Noncooperative Game Theory, 2nd Edition

Cited by 1,878 publications

References 0 publications

Incremental Sampling-Based Algorithms for a Class of Pursuit-Evasion Games

Incremental Sampling-Based Algorithms for a Class of Pursuit-Evasion Games

A Variational Formula for Stochastic Controls and Some Applications

Bicycle Routing for Maximum Suntan

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