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Advances in Dynamic Game Theory

Numerical Methods, Algorithms, and Applications to Ecology and Economics

  • Book
  • © 2007

Overview

Editors:
  1. Steffen Jørgensen

    1. Department of Economics and Business, University of Southern Denmark, Denmark

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  2. Marc Quincampoix

    1. Laboratoire de Mathématiques, Université de Bretagne Occidentale, France

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  3. Thomas L. Vincent

    1. Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, USA

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  • Collection of selected contributions giving a state-of-the-art account of recent developments in dynamic game theory and its applications
  • Covers a broad range of topics: stochastic and differential games; applications of dynamic games in various areas, such as ecology and economics; zero- and non-zero games; and pursuit-evasion games
  • Written by experts in their respective disciplines
  • Broad audience of researchers, practitioners, and advanced graduate students in applied mathematics and engineering

Part of the book series: Annals of the International Society of Dynamic Games (AISDG, volume 9)

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Table of contents (35 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Dynamic Game Theory

    1. Front Matter

      Pages 1-1
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    2. Differential Games Through Viability Theory: Old and Recent Results

      • Pierre Cardaliaguet, Marc Quincampoix, Patrick Saint-Pierre
      Pages 3-35

    3. Differential Games with Impulse Control

      • Arkadii A. Chikrii, Ivan I. Matychyn, Kirill A. Chikrii
      Pages 37-55

    4. On the Instability of the Feedback Equilibrium Payoff in a Nonzero-Sum Differential Game on the Line

      • Pierre Cardaliaguet
      Pages 57-67

    5. Application to Aircraft Control During Landing

      • S. A. Ganebny, S. S. Kumkov, V. S. Patsko, S. G. Pyatko
      Pages 69-92

    6. Games, Incompetence, and Training

      • Justin Beck, Jerzy A. Filar
      Pages 93-110

    7. StackelbergWell-Posedness and Hierarchical Potential Games

      • Marco Margiocco, Lucia Pusillo
      Pages 111-128

  3. Stochastic Differential Games

    1. Front Matter

      Pages 129-129
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    2. Ergodic Problems in Differential Games

      • Olivier Alvarez, Martino Bardi
      Pages 131-152

    3. Subgame Consistent Solutions for a Class of Cooperative Stochastic Differential Games with Nontransferable Payoffs

      • DavidW. K. Yeung, Leon Petrosyan, Patricia Melody Yeung
      Pages 153-170

  4. Pursuit-Evasion Games

    1. Front Matter

      Pages 170-170
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    2. Geometry of Pursuit-Evasion Games on Two-Dimensional Manifolds

      • Arik Melikyan
      Pages 173-194

    3. Solution of a Linear Pursuit-Evasion Game with Variable Structure and Uncertain Dynamics

      • Josef Shinar, Valery Y. Glizer, Vladimir Turetsky
      Pages 195-222

    4. Pursuit-Evasion Games with Impulsive Dynamics

      • Eva Crück, Marc Quincampoix, Patrick Saint-Pierre
      Pages 223-247

    5. Approaching Coalitions of Evaders on the Average

      • Igor Shevchenko
      Pages 249-268

  5. Evolutionary Game Theory and Applications

    1. Front Matter

      Pages 269-269
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    2. Adaptive Dynamics Based on Ecological Stability

      • József Garay
      Pages 271-286

    3. Adaptive Dynamics, Resource Conversion Efficiency, and Species Diversity

      • William A. Mitchell
      Pages 287-303

    4. Evolutionarily Stable Relative Abundance Distributions

      • Tania L. S. Vincent, Thomas L. Vincent
      Pages 305-326
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Economics and Business, University of Southern Denmark, Denmark

    Steffen Jørgensen

  • Laboratoire de Mathématiques, Université de Bretagne Occidentale, France

    Marc Quincampoix

  • Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, USA

    Thomas L. Vincent

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