Advances in Dynamic Games and Applications
Jerzy A. Filar, Vladimir Gaitsgory, Koichi Mizukami
Springer Science & Business Media, Mar 30, 2000 - Mathematics - 461 pages
Modem game theory has evolved enonnously since its inception in the 1920s in the works ofBorel and von Neumann and since publication in the 1940s of the seminal treatise "Theory of Games and Economic Behavior" by von Neumann and Morgenstern. The branch of game theory known as dynamic games is-to a significant extent-descended from the pioneering work on differential games done by Isaacs in the 1950s and 1960s. Since those early decades game theory has branched out in many directions, spanning such diverse disciplines as math ematics, economics, electrical and electronics engineering, operations research, computer science, theoretical ecology, environmental science, and even political science. The papers in this volume reflect both the maturity and the vitalityofmodem day game theoryin general, andofdynamic games, inparticular. The maturitycan be seen from the sophistication ofthe theorems, proofs, methods, and numerical algorithms contained in these articles. The vitality is manifested by the range of new ideas, new applications, the numberofyoung researchers among the authors, and the expanding worldwide coverage of research centers and institutes where the contributions originated.
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admissible algorithm Applications assume assumption asymptotically Basar bifurcation boundary bounded collision avoidance computed consider constraint control problem convergence convex corresponding cost function defined definition denote departure rate differential game disturbance attenuation domain driver Dynamic Games Dynkin formula equation evader exists feedback control Figure finite flow control game theory game value games with perfect geodesic arc given Hence inequality initial Lemma linear Markov Mathematics matrix minimal mixed strategies Nash equilibrium nonlinear nonnegative obtained optimal control optimal policies optimal strategy paper parameters payoff payoff matrix perfect information policy for Player preimages probability Proof Proposition pure strategies pursuer pursuit-evasion quadratic queue Riccati saddle point satisfies Section semicontinuous simulations singular surfaces singularly perturbed system solve stationary stationary policy step stochastic games strategy pair subgame theory trajectory unique value function variables vector viscosity solution weighted discounted zero-sum