47:. 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.
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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.
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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
178:
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
806:
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MarĂn-Solano, JesĂşs; Shevkoplyas, Ekaterina V. (December 2011). "Non-constant discounting and differential games with random time horizon".
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202:(SFNE). A recent example is the stochastic differential game of capitalism by Leong and Huang (2010). In 2016
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Differential Games: A Mathematical Theory with
Applications to Warfare and Pursuit, Control and Optimization
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Dynamic
Optimization : The Calculus of Variations and Optimal Control in Economics and Management
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and a single criterion to be optimized; differential game theory generalizes this to two controls
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688:"Optimal Interception of Evasive Missile Warheads: Numerical Solution of the Differential Game"
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are a group of problems related to the modeling and analysis of conflict in the context of a
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Differential Game Theory with
Applications to Missiles and Autonomous Systems Guidance
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Differential games have been applied to economics. Recent developments include adding
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641:"Comparison of Optimal Control and Differential Game Intercept Missile Guidance Laws"
523:
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Petrosjan, L.A.; Shevkoplyas, E.V. (2000). "Cooperative games with random duration".
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166:, publishing a text-book treatment in 1965. One of the first games analyzed was the
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Leong, C. K.; Huang, W. (2010). "A stochastic differential game of capitalism".
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28:
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Dockner, Engelbert; Jorgensen, Steffen; Long, Ngo Van; Sorger, Gerhard (2001),
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Petrosjan, L.A.; Murzov, N.V. (1966). "Game-theoretic problems of mechanics".
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for his contributions to the analysis of continuous-time dynamic games using
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801:, Series on Optimization, vol. 2, World Scientific Publishers,
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Djehiche, Boualem; Tcheukam, Alain; Tembine, Hamidou (2017-09-27).
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162:. The first to study the formal theory of differential games was
158:, differential games have been employed since a 1925 article by
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problems. In an optimal control problem there is single control
408:
Roos, C. F. (1925). "A Mathematical Theory of
Competition".
598:"Linear–Quadratic Mean-Field-Type Games: A Direct Method"
781:
Differential Games in
Economics and Management Science
223:
Additionally, differential games have applications in
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65:
832:. Department of Mathematics, Penn State University.
752:"Simple-motion pursuit–evasion differential games"
138:
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198:to differential games and the derivation of the
827:"Noncooperative Differential Games: A Tutorial"
451:(Dover ed.). London: John Wiley and Sons.
387:. Amsterdam: North-Holland. pp. 272–288.
182:function. Therefore, the players maximize the
43:or variables evolve over time according to a
8:
55:Differential games are related closely with
322:AIMS Electronics and Electrical Engineering
18:Differential games with random time horizon
692:Journal of Guidance, Control, and Dynamics
686:Pontani, Mauro; Conway, Bruce A. (2008).
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318:"Mean-Field-Type Games in Engineering"
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200:stochastic feedback Nash equilibrium
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539:Journal of Mathematical Economics
139:{\displaystyle u_{1}(t),u_{2}(t)}
524:10.1016/j.automatica.2011.09.010
238:differential games see Pachter.
645:Journal of Guidance and Control
573:"American Economic Association"
411:American Journal of Mathematics
272:Tembine, Hamidou (2017-12-06).
783:, Cambridge University Press,
493:Vestnik of St.Petersburg Univ.
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799:Differential Games of Pursuit
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379:; Schwartz, Nancy L. (1991).
213:American Economic Association
51:Connection to optimal control
639:Anderson, Gerald M. (1981).
729:. Aerospace Series. Wiley.
344:10.3934/ElectrEng.2017.1.18
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725:Faruqi, Farhan A. (2017).
168:'homicidal chauffeur game'
461:– via Google Books.
852:Game theory game classes
797:Petrosyan, Leon (1993),
248:Lotka–Volterra equations
180:probability distribution
39:. More specifically, a
445:Isaacs, Rufus (1999) .
291:10.3934/Math.2017.4.706
274:"Mean-field-type games"
184:mathematical expectancy
750:Pachter, Meir (2002).
253:Mean-field game theory
208:John Bates Clark Medal
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45:differential equation
825:(December 8, 2010).
381:"Differential Games"
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81:{\displaystyle u(t)}
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704:2008JGCD...31.1111C
657:1981JGCD....4..109A
218:stochastic calculus
174:Random time horizon
229:autonomous systems
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33:differential games
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790:978-0-521-63732-9
764:on July 20, 2011.
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518:(12): 2626–2638.
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512:Automatica
480:: 423–433.
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220:methods.
210:from the
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242:See also
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150:History
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348:S2CID
330:arXiv
259:Notes
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669:ISSN
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227:and
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