Advances in Dynamic Game Theory

This collection of selected contributions gives an account of recent developments in dynamic game theory and its applications, covering both theoretical advances and new applications of dynamic games in such areas as pursuit-evasion games, ecology, and economics. Written by experts in their respective disciplines, the chapters are an outgrowth of presentations from the 11th International Symposium on Dynamic Games and Applications.

Key topics covered include:

• stochastic and differential games

• dynamic games and their applications in various areas, such as ecology and economics

• numerical methods and algorithms in dynamic games

• zero- and nonzero-sum games

• pursuit-evasion games

• evolutionary game theory and applications

The work will serve as a state-of-the art account of recent advances in dynamic game theory and its applications for researchers, practitioners, and advanced students in applied mathematics, mathematical finance, and engineering.

Résumé
The theory of dynamic games continues to evolve, and one purpose of this volume is to report a number of recent theoretical advances in the ?eld, which are covered in Parts I, II and IV. Another aim of this work is to present some new applications of dynamic games in various areas, including pursuit-evasion games (Part III), ecology (Part IV), and economics (Part V). The volume concludes with a number of contributions in the ?eld of numerical methods and algorithms in dynamic games (Part VI). With a single exception, the contributions of this volume are outgrowths of talks that were presented at the Eleventh International Symposium on Dynamic Games and Applications, held in Tucson, Arizona, USA, in December 2004, and organized by the International Society of Dynamic Games. The symposium was co-sponsored by the University of Arizona, College of Engineering and Aerospace and Mechanical Engineering, as well as GERAD, Montréal, Canada, and the ISDG Organizing Society. The volume contains thirty-?ve chapters that have been peer-reviewed according to the standards of international journals in game theory and applications. Part I deals with the theory of dynamic games and contains six chapters. Cardaliaguet, Quincampoix, and Saint-Pierre provide a survey of the state-- the-art of the use of viability theory in the formulation and analysis of differential games, in particular zero-sum games. An important result of viability theory is that many zero-sum differential games can be formulated as viability problems.

Contenu
Dynamic Game Theory.- Differential Games Through Viability Theory: Old and Recent Results.- Differential Games with Impulse Control.- On the Instability of the Feedback Equilibrium Payoff in a Nonzero-Sum Differential Game on the Line.- Application to Aircraft Control During Landing.- Games, Incompetence, and Training.- StackelbergWell-Posedness and Hierarchical Potential Games.- Stochastic Differential Games.- Ergodic Problems in Differential Games.- Subgame Consistent Solutions for a Class of Cooperative Stochastic Differential Games with Nontransferable Payoffs.- Pursuit-Evasion Games.- Geometry of Pursuit-Evasion Games on Two-Dimensional Manifolds.- Solution of a Linear Pursuit-Evasion Game with Variable Structure and Uncertain Dynamics.- Pursuit-Evasion Games with Impulsive Dynamics.- Approaching Coalitions of Evaders on the Average.- Evolutionary Game Theory and Applications.- Adaptive Dynamics Based on Ecological Stability.- Adaptive Dynamics, Resource Conversion Efficiency, and Species Diversity.- Evolutionarily Stable Relative Abundance Distributions.- Foraging Under Competition: Evolutionarily Stable Patch-Leaving Strategies with Random Arrival Times..- Foraging Under Competition: Evolutionarily Stable Patch-Leaving Strategies with Random Arrival Times.- Evolution of Corn Oil Sensitivity in the Flour Beetle.- The Evolution of Gut Modulation and Diet Specialization as a Consumer-Resource Game.- Applications of Dynamic Games to Economics.- Time-Consistent Fair Water Sharing Agreements.- A Hybrid Noncooperative Game Model for Wireless Communications.- Incentive-Based Pricing for Network Games with Complete and Incomplete Information.- Incentive Stackelberg Strategies for a Dynamic Game on Terrorism.- Capital Accumulation, Mergers, and the Ramsey Golden Rule.- Economic Growth and Process Spillovers with Step-by-Step Innovation.- Supplier-Manufacturer Collaboration onNew Product Development.- A Differential Game of a Dual Distribution Channel.- Design Imitation in the Fashion Industry.- Formulating and Solving Service Network Pricing and Resource Allocation Games as Differential Variational Inequalities.- Numerical Methods and Algorithms in Dynamic Games.- Numerical Methods for Stochastic Differential Games: The Ergodic Cost Criterion.- Gradient Transformation Trajectory Following Algorithms for Determining Stationary Min-Max Saddle Points.- Singular Perturbation Trajectory Following Algorithms for Min-Max Differential Games.- Min-Max Guidance Law Integration.- Agent-Based Simulation of the N-Person Chicken Game.- The Optimal Trajectory in the Partial-Cooperative Game.