Advances in Dynamic Games and Applications

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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This text focuses on various aspects of dynamic game theory, and serves as a guide to the vitality of the field and its applications. A variety of topics are presented including: robust control design and H infinity; pursuit-evasion games; and coupled dynamic and stochastic games.

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I Robust Control Design and H?.- Worst-Case Rate-Based Flow Control with an ARMA Model of the Available Bandwidth.- H? Output Feedback Control Problems for Bilinear Systems.- H? Control of a Class of Infinite-Dimensional Linear Systems with Nonlinear Outputs.- Nonstandard Extension of H?-Optimal Control for Singularly Perturbed Systems.- II Pursuit-Evasion (P-E) Games.- Geodesic Parallel Pursuit Strategy in a Simple Motion Pursuit Game on the Sphere.- Real-Time Collision Avoidance: Differential Game, Numerical Solution, and Synthesis of Strategies.- Rendezvous-Evasion as a Multistage Game with Observed Actions.- Identification and Construction of Singular Surfaces in Pursuit-Evasion Games.- On the Numerical Solution of a Class of Pursuit-Evasion Games.- III Coupled Dynamic and Stochastic Games.- Infinite Horizon Dynamic Games with Coupled State Constraints.- Constrained Markov Games: Nash Equilibria.- Piecewise-Deterministic Differential Games and Dynamic Teams with Hybrid Controls.- A Game Variant of the Stopping Problem on Jump Processes with a Monotone Rule.- IV General Game Theoretic Developments.- Refinement of the Nash Solution for Games with Perfect Information.- A Perturbation on Two-Person Zero-Sum Games.- The Linear Complementarity Problem in Static and Dynamic Games.- Weighted Discounted Stochastic Games with Perfect Information.- Stochastic Games with Complete Information and Average Cost Criteria.- V Applications.- Crime and Law Enforcement: A Multistage Game.- Global Analysis of a Dynamic Duopoly Game with Bounded Rationality.- A Multistage Supergame of Downstream Pollution.- Solution and Stability for a Simple Dynamic Bottleneck Model.- Cumulants and Risk-Sensitive Control: A Cost Mean and Variance Theory with Application to Seismic Protection ofStructures.