Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics

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Steffen Jorgensen, Marc Quincampoix, Thomas L. Vincent
Springer Science & Business Media, Nov 15, 2007 - Mathematics - 718 pages
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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.
 

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Contents

Old and Recent Results
3
Differential Games with Impulse Control
36
On the Instability of the Feedback Equilibrium Payoff in a NonzeroSum Differential Game on the Line
57
Application to Aircraft Control During Landing
68
Games Incompetence and Training
93
Stackelberg WellPosedness and Hierarchical Potential Games
111
Stochastic Differential Games
129
Ergodic Problems in Differential Games
131
The Evolution of Gut Modulation and Diet Specialization as a ConsumerResource Game
377
Applications of Dynamic Games to Economics
391
TimeConsistent Fair Water Sharing Agreements
393
A Hybrid Noncooperative Game Model for Wireless Communications
411
IncentiveBased Pricing for Network Games with Complete and Incomplete Information
430
Incentive Stackelberg Strategies for a Dynamic Game on Terrorism
459
Capital Accumulation Mergers and the Ramsey Golden Rule
487
Economic Growth and Process Spillovers with StepbyStep Innovation
507

Subgame Consistent Solutions for a Class of Cooperative Stochastic Differential Games with Nontransferable Payoffs
153
PursuitEvasion Games
171
Geometry of PursuitEvasion Games on TwoDimensional Manifolds
172
Solution of a Linear PursuitEvasion Game with Variable Structure and Uncertain Dynamics
195
PursuitEvasion Games with Impulsive Dynamics
223
Approaching Coalitions of Evaders on the Average
249
Evolutionary Game Theory and Applications
269
Adaptive Dynamics Based on Ecological Stability
270
Adaptive Dynamics Resource Conversion Efficiency and Species Diversity
287
Evolutionarily Stable Relative Abundance Distributions
305
Evolutionarily Stable PatchLeaving Strategies with Random Arrival Times 1 Scramble Competition
327
Foraging Under Competition Evolutionarily Stable PatchLeaving Strategies with Random Arrival Times
349
Evolution of Corn Oil Sensitivity in the Flour Beetle
366
SupplierManufacturer Collaboration on New Product Development
527
A Differential Game of a Dual Distribution Channel
546
Design Imitation in the Fashion Industry
569
Formulating and Solving Service Network Pricing and Resource Allocation Games as Differential Variational Inequalities
587
Numerical Methods and Algorithms in Dynamic Games
615
The Ergodic Cost Criterion
617
Algorithms for Determining Stationary MinMax Saddle Points
638
Singular Perturbation Trajectory Following Algorithms for MinMax Differential Games
659
MinMax Guidance Law Integration
679
AgentBased Simulation of the NPerson Chicken Game
695
The Optimal Trajectory in the PartialCooperative Game
704
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About the author (2007)

Dr Vincent is Professor Emeritus with the Aerospace and Mechanical Engineering at the University of Arizona. His main research interests are in the area of Nonlinear Control System Design, Optimal Control and Game Theory, and Evolution and Adaptation of Biological Systems. He has 153 publications including 79 journal articles, and 8 books.