New Trends in Dynamic Games and Applications

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.

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I. Minimax control.- Expected Values, Feared Values, and Partial Information Optimal Control.- H?-Control of Nonlinear Singularly Perturbed Systems and Invariant Manifolds.- A Hybrid (Differential-Stochastic) Zero-Sum Game with Fast Stochastic Part.- H?-Control of Markovian Jump Systems and Solutions to Associated Piecewise-Deterministic Differential Games.- The Big Match on the Integers.- II. Pursuit evasion.- Synthesis of Optimal Strategies for Differential Games by Neural Networks.- A Linear Pursuit-Evasion Game with a State Constraint for a Highly Maneuverable Evader.- Three-Dimensional Air Combat: Numerical Solution of Complex Differential Games.- Control of Informational Sets in a Pursuit Problem.- Decision Support System for Medium Range Aerial Duels Combining Elements of Pursuit-Evasion Game Solutions with AI Techniques.- Optimal Selection of Observation Times in a Costly Information Game.- Pursuit Games with Costly Information: Application to the ASW Helicopter Versus Submarine Game.- Linear Avoidance in the Case of Interaction of Controlled Objects Groups.- III. Solution methods.- Convergence of Discrete Schemes for Discontinuous Value Functions of Pursuit-Evasion Games.- Undiscounted Zero Sum Differential Games with Stopping Times.- Guarantee Result in Differential Games with Terminal Payoff.- IV. Nonzero-sum games, theory.- Lyapunov Iterations for Solving Coupled Algebraic Riccati Equations of Nash Differential Games and the Algebraic Riccati Equation of Zero-Sum Games.- A Turnpike Theory for Infinite Horizon Open-Loop Differential Games with Decoupled Controls.- Team-Optimal Closed-Loop Stackelberg Strategies for Discrete-Time Descriptor Systems.- On Independence of Irrelevant Alternatives and Dynamic Programming in Dynamic Bargaining Games.- The Shapley Value for Differential Games.- V. Nonzero-sum games, applications.- Dynamic Game Theory and Management Strategy.- Endogenous Growth as a Dynamic Game.- Searching for Degenerate Dynamics in Animal Conflict Game Models involving Sexual Reproduction.