Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and EconomicsSteffen Jorgensen, Marc Quincampoix, Thomas L. Vincent 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. |
Contents
| 3 | |
Pierre Cardaliaguet Marc Quincampoix and Patrick SaintPierre | 36 |
Arkadii A Chikrii Ivan I Matychyn and Kirill A Chikrii | 57 |
Games Incompetence and Training | 93 |
Justin Beck and Jerzy A Filar | 111 |
Ergodic Problems in Differential Games | 131 |
Stochastic Differential Games with Nontransferable Payoffs | 153 |
Geometry of PursuitEvasion Games on TwoDimensional Manifolds 173 | 172 |
as a ConsumerResource Game | 377 |
TimeConsistent Fair Water Sharing Agreements | 393 |
Rodney Beard and Stuart McDonald | 411 |
Tansu Alpcan and Tamer Basar | 430 |
Hongxia Shen and Tamer Basar | 459 |
Capital Accumulation Mergers and the Ramsey Golden Rule | 487 |
Roberto Cellini and Luca Lambertini | 507 |
SupplierManufacturer Collaboration on New Product Development | 527 |
Solution of a Linear PursuitEvasion Game | 195 |
PursuitEvasion Games with Impulsive Dynamics | 223 |
Eva Crück Marc Quincampoix and Patrick SaintPierre | 249 |
Adaptive Dynamics Based on Ecological Stability 271 | 270 |
Adaptive Dynamics Resource Conversion Efficiency | 287 |
Evolutionarily Stable Relative Abundance Distributions | 305 |
Evolutionarily Stable PatchLeaving | 327 |
Strategies with Random Arrival Times 2 Interference Competition | 349 |
Frédéric Hamelin Pierre Bernhard A J Shaiju and Éric Wajnberg | 366 |
Bowon Kim and Fouad El Ouardighi | 546 |
Design Imitation in the Fashion Industry | 569 |
Steffen Jørgensen and Andrea Di Liddo | 587 |
Gradient Transformation Trajectory Following Algorithms | 638 |
Singular Perturbation Trajectory Following Algorithms | 659 |
MinMax Guidance Law Integration | 679 |
AgentBased Simulation of the NPerson Chicken Game | 695 |
The Optimal Trajectory in the PartialCooperative Game 705 | 704 |
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Common terms and phrases
adaptive algorithm analysis Applications approach approximation assume assumption attacks called choose coalition competition condition consider consistent constant constraints continuous cooperative corresponding cost decrease defined Definition demand denote depends derivative described determined differential games distribution domain dynamics Economics effect efficiency effort equal equation equilibrium example exists Figure firm fitness fixed foraging function given Hence holds impulse incentive increasing individual initial introduced lead linear lower maximal means method Nash Note obtained optimal parameter patch payoff period player population positive possible problem profit Proof Proposition provides relative resident resource respect satisfies selection solution space species stable Stackelberg strategy terminal terror terrorists Theorem theory trajectory unique University variable vector West yields