Differential game
In game theory, differential games are a group of problems related to the modeling and analysis of conflict in the context of a dynamical system. More specifically, a state variable or variables evolve over time according to a differential equation. Early analyses reflected military interests, considering two actors - the pursuer and the evader - with diametrically opposed goals. More recent analyses have reflected engineering or economic considerations.
Contents
Connection to optimal control
Differential games are related closely with optimal control problems. In an optimal control problem there is single control 
and a single criterion to be optimized; differential game theory generalizes this to two controls 
and two criteria, one for each player. Each player attempts to control the state of the system so as to achieve its goal; the system responds to the inputs of all players.
History
The first to study differential games was Rufus Isaacs (1951, published 1965)[1] and one of the first games analyzed was the 'homicidal chauffeur game'.
Applications
Differential games have been applied to economics. Recent developments include adding stochasticity to differential games and the derivation of the stochastic feedback Nash equilibrium (SFNE). A recent example is the stochastic differential game of capitalism by Leong and Huang (2010).[2]
For a survey of pursuit-evasion differential games see Pachter.[3]
Notes
- ↑ Rufus Isaacs, Differential Games, Dover, 1999. ISBN 0-486-40682-2 Google Books
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- ↑ Meir Pachter: Simple-motion pursuit-evasion differential games, 2002
Textbooks and general references
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External links
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