MIT16_410F10_lec25

MIT16_410F10_lec25 - 16.410/413 Principles of Autonomy and...

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16.410/413 Principles of Autonomy and Decision Making Lecture 25: Differential Games Sertac Karaman Massachusetts Institute of Technology December. 8, 2010 S. Karaman ( MIT) L25: Differential Games December 8, 2010 1 / 32
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Outline Game theory and sequential games (recap previous lecture) Dynamical (control) systems and optimal control Dynamic Game Theory Numerical Methods A special case: Pursuit-evasion. S. Karaman ( MIT) L25: Differential Games December 8, 2010 3 / 32
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Game theory (Recap) Zero-sum Games Gains/losses of each player is balanced by the gains/losses of the all the other players. Cooperative vs. non-cooperative. Cooperative if groups of players may enforce binding agreements. Nash equilibrium No player can gain more by unilaterally changing strategy. An example Remember the prisoner’s dilemma: Player B cooperates Player B defects Player A cooperates (-1,-1) (-10, 0) Player A defects (0,-10) (-5,-5) Non-zero sum. Cooperation could have been enforced; otherwise may or may not arise. S. Karaman ( MIT) L25: Differential Games December 8, 2010 5 / 32
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Game Theory (Recap) Zero-sum Two-player Sequential games Key characteristics Two players Zero-sum reward Sequential moves (from a finite set) Perfect information Terminates in a finite number of steps We have used alpha-beta pruning to solve such games. Today, we will study non-cooperative dynamic games . S. Karaman ( MIT) L25: Differential Games December 8, 2010 6 / 32
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Dynamic games Dynamic games: Actions available to each agent depends on its current state which evolves according to a certain dynamical system. Sets of states/actions is usually a continuum. In many cases, the agents involved in the game are subject to dynamics. Some (major/relevant) application areas: Dogfight Aircraft landing subject to wind (or other) disturbance Air traffic control Economics & Management Science S. Karaman ( MIT) L25: Differential Games December 8, 2010 7 / 32
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History of Dynamic Games Introduction of dynamic games is attributed to Rufus Isaacs (1951). Book : R. Isaacs, Differential Games: A mathematical theory with applications to warfare and pursuit, control and optimization, 1965. Later the theory was developed by many contributors including A. Merz and J. Breakwell. More recent contributions by T. Basar and coworkers. Book : Basar and Olsder, Dynamic Noncooperative Game Theory, 1982. S. Karaman ( MIT) L25: Differential Games December 8, 2010 8 / 32
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Dynamic Games Literature Dynamic games has a very rich literature. S. Karaman ( MIT) L25: Differential Games December 8, 2010 9 / 32 Images of book covers removed due to copyright restrictions: Isaacs, Rufus. Differential Games: A Mathematical Theory with Applications to Warfare, Pursuit, Control and Optimization. Dover, 1999. ISBN: 9780486406824. Basar, Tamer, and Geert Jan Olsder. Dynamic Noncooperative Game Theory . 2nd ed. SIAM, 1999. ISBN: 9780898714296. Dockner, Engelbert, Steffen Jorgensen, Ngo Van Long, and Gerhard Sorger. Differential Games in Economics and Management Science.
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MIT16_410F10_lec25 - 16.410/413 Principles of Autonomy and...

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