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Pursuit evasion game for an airplane using the rrt infeasible
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
Differential game
Connection to optimal control
Differential games are related closely with optimal control problems. In an optimal control problem there is single control
History
The first to study differential games was Rufus Isaacs (1951, published 1965) and one of the first games analyzed was the 'homicidal chauffeur game'.
Random time horizon
Games with a random time horizon are a particular case of differential games. In such games, the terminal time is a random variable with a given probability distribution function. Therefore, the players maximize the mathematical expectancy of the cost function. It was shown that the modified optimization problem can be reformulated as a discounted differential game over an infinite time interval
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).
For a survey of pursuit-evasion differential games see Pachter.