Stability Concept of Evolutionary Game Theory : A Dynamic Approach

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.