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. The problem usually consists of two actors, a pursuer and an evader, with conflicting goals. The dynamics of the pursuer and the evader are modeled by systems of differential equations.
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 his goal; the system responds to the inputs of both players.
The first to study differential games was Rufus Isaacs (1951, published 1965) and one of the first games analyzed was the 'homicidal chauffeur game'.
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).
Read more about Differential Game: Applications
Famous quotes containing the words differential and/or game:
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)
“My first big mistake was made when, in a moment of weakness, I consented to learn the game; for a man who can frankly say “I do not play bridge” is allowed to go over in the corner and run the pianola by himself, while the poor neophyte, no matter how much he may protest that he isn’t “at all a good player, in fact I’m perfectly rotten,” is never believed, but dragged into a game where it is discovered, too late, that he spoke the truth.”
—Robert Benchley (1889–1945)