New Trends in Dynamic Games and Applications : Annals of the International Society of Dynamic Games Volume 3

The theory of dynamic games is very rich in nature and very much alive! If the reader does not already agree with this statement, I hope he/she will surely do so after having consulted the contents of the current volume. The activities which fall under the heading of 'dynamic games' cannot easily be put into one scientific discipline. On the theoretical side one deals with differential games, difference games (the underlying models are described by differential, respec­ tively difference equations) and games based on Markov chains, with determin­ istic and stochastic games, zero-sum and nonzero-sum games, two-player and many-player games - all under various forms of equilibria. On the practical side, one sees applications to economics (stimulated by the recent Nobel prize for economics which went to three prominent scientists in game theory), biology, management science, and engineering. The contents of this volume are primarily based on selected presentations made at the Sixth International Symposium on Dynamic Games and Applica­ tions, held in St Jovite, Quebec, Canada, 13-15 July 1994. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival technical journals. This conference, as well as its predecessor which was held in Grimentz, 1992, took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. One of the activities of the ISDG is the publication of these Annals. The contributions in this volume have been grouped around five themes. Front Matter....Pages i-xi Front Matter....Pages 1-1 Expected Values, Feared Values, and Partial Information Optimal Control....Pages 3-24 H ∞ -Control of Nonlinear Singularly Perturbed Systems and Invariant Manifolds....Pages 25-45 A Hybrid (Differential-Stochastic) Zero-Sum Game with a Fast Stochastic Part....Pages 47-59 H∞-Control of Markovian Jump Systems and Solutions to Associated Piecewise-Deterministic Differential Games....Pages 61-94 The Big Match on the Integers....Pages 95-107 Front Matter....Pages 109-109 Synthesis of Optimal Strategies for Differential Games by Neural Networks....Pages 111-141 A Linear Pursuit-Evasion Game with a State Constraint for a Highly Maneuverable Evader....Pages 143-164 Three-Dimensional Air Combat: Numerical Solution of Complex Differential Games....Pages 165-190 Control of Informational Sets in a Pursuit Problem....Pages 191-206 Decision Support System for Medium Range Aerial Duels Combining Elements of Pursuit-Evasion Game Solutions with AI Techniques....Pages 207-225 Optimal Selection of Observation Times in a Costly Information Game....Pages 227-246 Pursuit Games with Costly Information: Application to the ASW Helicopter Versus Submarine Game....Pages 247-257 Linear Avoidance in the Case of Interaction of Controlled Objects Groups....Pages 259-269 Front Matter....Pages 271-271 Convergence of Discrete Schemes for Discontinuous Value Functions of Pursuit-Evasion Games....Pages 273-304 Undiscounted Zero Sum Differential Games with Stopping Times....Pages 305-322 Guaranteed Result in Differential Games with Terminal Payoff....Pages 323-330 Front Matter....Pages 331-331 Lyapunov Iterations for Solving Coupled Algebraic Riccati Equations of Nash Differential Games and Algebraic Riccati Equations of Zero-Sum Games....Pages 333-351 A Turnpike Theory for Infinite Horizon Open-Loop Differential Games with Decoupled Controls....Pages 353-376 Team-Optimal Closed-Loop Stackelberg Strategies for Discrete-Time Descriptor Systems....Pages 377-394 On Independence of Irrelevant Alternatives and Dynamic Programming in Dynamic Bargaining Games....Pages 395-408 Front Matter....Pages 331-331 The Shapley Value for Differential Games....Pages 409-417 Front Matter....Pages 419-419 Dynamic Game Theory and Management Strategy....Pages 421-437 Endogenous Growth as a Dynamic Game....Pages 439-465 Searching for Degenerate Dynamics in Animal Conflict Game Models involving Sexual Reproduction....Pages 467-482 Back Matter....Pages 483-483