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Stability Concept of Evolutionary Game Theory : A Dynamic Approach : Lecture Notes in Biomathematics - Ross Cressman

Stability Concept of Evolutionary Game Theory : A Dynamic Approach

Lecture Notes in Biomathematics

Paperback ISBN: 9783540554196
Number Of Pages: 129

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This book considers, in detail, the game-theoretic effects of contestant information and two-species interactions. Of major significance to evolutionary biologists are the dynamic consequences, on the evolutionary process, of territorial ownership or repeated interactions betweem the same individuals. The book is intended as a text/reference for students/researchers in either discipline (evolutionary biology or game theory) who have a minimum mathematical maturity of a senior undergraduate.

1. Introduction.- 2. Frequency-Dependent Evolution in a Single Haploid Species.- 1. Pure and Mixed Strategies.- 2. Monomorphic ESS's and Stability.- 3. The Hawk-Dove Game.- 4. The Static Characterization of an ESS.- (A) Biological Considerations.- (B) Mathematical Considerations.- 5. Stability for the Continuous Dynamic.- 6. The Strong Stability Concept and the Dynamic Characterization of an ESS.- 7. Stability for the Discrete Dynamic.- 8. Alternative Proof of Theorem 2.5.2.- (A) The Centre Manifold for the Pure-Strategy Dynamic.- (B) The Centre Manifold for the Mixed-Strategy Dynamic.- 9. Nonlinear Fitness Functions.- (A) The Sex-Ratio Game.- (B) ESS's and Stability.- 10. Appendix on Centre Manifold Theory.- 3. Frequency-Dependent Evolution in a Two-Species Haploid System.- 1. Frequency-Dependent Fitness.- 2. Monomorphic ESS's and Stability.- 3. Examples: Battle-of-the-Sexes and Edgeworth Market Games.- (A) Battle-of-the Sexes.- (B) Edgeworth Market Games.- 4. The Static Characterization of a Two-Species ESS.- 5. Strong Stability for the Continuous Dynamic.- 6. Multi-Species Frequency-Dependent Evolution.- 4. Frequency-Dependent Evolution in a Randomly-Mating Diploid Species.- 1. Natural Selection as an Evolutionary Game.- (A) The Frequency-Dependent Haploid Perspective.- (B) The Frequency-Independent Diploid Perspective.- 2. Single-Locus Models.- 3. Two-Phenotype, Frequency-Dependent Evolution at a Single Locus.- 4. Multi-Phenotype, Frequency-Dependent Evolution at a Single Locus.- (A) Examples.- (B) Linearization.- 5. A Two-Locus, Two-Allele, Two-Phenotype Example.- 5. Frequency- and Density-Dependent Evolution in a Haploid Species.- 1. Frequency- and Density-Dependent Fitness (and the Haploid Dynamic).- 2. Monomorphic DDESS's and Stability.- 3. The Density-Dependent Hawk-Dove Game.- (A) Non-Aggressive Behavior Enhanced at High Density.- (B) Aggressive Behavior Enhanced at High Density.- 4. The DDESS Conditions and Strong Stability.- 5. Density-Dependent Natural Selection as a Haploid Evolutionary Game.- 6. Evolutionary Stability in Multi-Species Population-Dynamic Models.- An Intermission.- 6. Evolutionary Stable Sets and Contestant Information.- 1. A Mixed-Strategy Hawk-Dove Game.- 2. The Static Characterization of an ES Set.- 3. The Dynamic Characterization of an ES Set.- 4. The Hawk-Dove Game with Varying Resource.- 5. ES Sets for Games in Extensive Form.- 6. The Owner-Intruder Game.- (A) A Single-Species Extensive-Game Perspective.- (B) The Two-Species Perspective.- 7. Multi-Stage Games.- (A) A Two-Trial Game.- (B) The Iterated Prisoner's Dilemma Game.- 7. References.- 8. Index.

ISBN: 9783540554196
ISBN-10: 354055419X
Series: Lecture Notes in Biomathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 129
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.41 x 16.99  x 0.76
Weight (kg): 0.24