Differential Games

Lewin, Joseph

doi:10.1007/978-1-4471-2065-0

Cited by 57 publications

(5 citation statements)

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“…Much of the economic analysis of conflict relies on game theory as an analytical tool. 1 When elements of control theory are integrated into a classical non-cooperative game, we obtain a di erential game (Lewin 1994). These models are of high interest, but fraught with two problems: first, the resulting systems of di erential equations frequently do not a ord an analytical solution (Ruth and Hannon 2012), in particular if the equations of motion contain nonlinearities (Beckmann und Reimer 2014).…”

Section: Introductionmentioning

confidence: 99%

Bounded Rationality in Differential Games

Beckmann

2017

SSRN Journal

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Section: Introductionmentioning

confidence: 99%

Bounded Rationality in Differential Games

Beckmann

2017

SSRN Journal

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“…Two person zero-sum differential games was originated by Isaac [12]. Since then, a number of books that relates to this area have been published such as Friedman [5], Pontryagin [19], Krasovkii and Subbotin [14], Petrosyan [18], Lewin [17], Chikrii [3], Grigorenko [6], Satimov [22].…”

Section: Introductionmentioning

confidence: 99%

Effective Pursuit Strategies in Simple Motion Differential Game of Three Pursuers and One Evader

Ibragimov¹,

Yunus²,

Alias³

2016

Int. J. of Pure and Appl. Math.

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“…Therefore, we need a dynamic game approach to study the interaction between dynamic traffic assignment and signal control. Differential game theory, one branch of this game theory (Isaacs, 1965;Lewin, 1994;Thoma and Wyner, 1991), provides a good framework for the combined problem, where it is assumed that the behavior of the system can be modeled as a system of ordinary differential equations. Differential game theory can be used to model situations where several interacting agents make strategic dynamic decisions.…”

Section: Introductionmentioning

confidence: 99%

A Differential Game Modeling Approach to Dynamic Traffic Assignment and Signal Control

Shi

2003

European Journal of Transport and Infrastructure Research

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This paper addresses a theoretical issue related to combined dynamic traffic assignment and signal control under conditions of congestion through a brief review of previous research and the discussion on interaction between dynamic traffic assignment and signal control. The dynamic characteristics of the interaction are approached using a differential game modeling approach here to formulate the decision-making process for solving the problem inherent in this combination. Specifically, the combined dynamic traffic assignment and signal control problem is formulated as a leader−follower differential game, where a leader and multiple followers engage interactively to finding optimal strategies under the assumption of an openloop information structure. Discretization in time is used to find a numerical solution for the proposed game model, and a simulated annealing algorithm is applied to obtain optimal strategies. Finally, a simulation study is conducted on a simple traffic network in which numerical results demonstrate the effectiveness of the proposed approach.

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Differential Games

Cited by 57 publications

References 0 publications

Bounded Rationality in Differential Games

Bounded Rationality in Differential Games

Effective Pursuit Strategies in Simple Motion Differential Game of Three Pursuers and One Evader

A Differential Game Modeling Approach to Dynamic Traffic Assignment and Signal Control

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