Advances in Dynamic Games and Applications

Game theory is a rich and active area of research of which this new volume of the Annals of the International Society of Dynamic Games is yet fresh evidence. Since the second half of the 20th century, the area of dynamic games has man­ aged to attract outstanding mathematicians, who found exciting open questions requiring tools from a wide variety of mathematical disciplines; economists, so­ cial and political scientists, who used game theory to model and study competition and cooperative behavior; and engineers, who used games in computer sciences, telecommunications, and other areas. The contents of this volume are primarily based on selected presentation made at the 8th International Symposium of Dynamic Games and Applications, held in Chateau Vaalsbroek, Maastricht, the Netherlands, July 5-8, 1998; this conference took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. The conference has been cosponsored by the Control Systems Society of the IEEE, IFAC (International Federation of Automatic Con­ trol), INRIA (Institute National de Recherche en Informatique et Automatique), and the University of Maastricht. One ofthe activities of the ISDG is the publica­ tion of the Annals. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival journals.

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Preface Contributers Part I. Dynamic Games: Theory On Problems with Information in Some Games: Modelling the Strategies in Some Dynamic Games A Historical Perspective on Cooperative Differential Games Certainty Equivalence Principle and Minimax Team Problems Evolutionary Processes in Signaling Games: The Impact of Different Learning Schemes Mixed Strategies for Hierarchical Zero-Sum Games The Existence and Uniqueness of Equilibria in Convex Games with Strategies in Hilbert Spaces Part II. Stochastic Games Existence of Equilibrium Payoffs in Two-Player Stochastic Games Persistently Good Strategies for Nonleavable Stochastic Games with Finite State Space On Stochastic Hybrid Zero-Sum Games with Nonlinear Slow Dynamics On Multichain Markov Games Perturbed Zero-Sum Games with Applications to Stochastic and Repeated Games Part III. Solution Methods of Dynamic Games Construction of Singular Surfaces Parallel Algorithms for the Isaacs Equation Computation of S-adapted Equilibria in Piecewise Deterministic Games via Stochastic Programming Methods Comparison of Two Numerical Approaches for the Barrier and Value of a Simple Pursuit-Evasion Game Part IV. Dynamic Games: Applications On Optimal Missile Guidance Upgrades with Dynamic Stackelberg Game Lineariztions Homicidal Chauffeur Game: Computation of Level Sets of the Value Function 'The Tragedy of the Commons' Modelled by Large Games