Evolutionary dynamics and extensive form games

Evolutionary game theory attempts to predict individual behavior (whether of humans or other species) when interactions between individuals are modeled as a noncooperative game. Most dynamic analyses of evolutionary games are based on their normal forms, despite the fact that many interesting games are specified more naturally through their extensive forms. Because every extensive form game has a normal form representation, some theorists hold that the best way to analyze an extensive form game is simply to ignore the extensive form structure and study the game in its normal form representation. This book rejects that suggestion, arguing that a game's normal form representation often omits essential information from the perspective of dynamic evolutionary game theory.

The book offers a synthesis of current knowledge about extensive form games from an evolutionary perspective, emphasizing connections between the extensive form representation and dynamic models that traditionally have been applied to biological and economic phenomena. It develops a general theory to analyze dynamically arbitrary extensive form games and applies this theory to a range of examples. It lays the foundation for the analysis of specific extensive form models of behavior and for the further theoretical study of extensive form evolutionary games.

Contents

• Introduction
  • Extensive Form versus Normal Form
  • Biology versus Economics
  • Imitation
  • Organizational Matters
  • Notes
• Symmetric Normal Form Games
  • The Replicator Dynamic
  • Dynamics for Two-Strategy Games
  • Monotone Selection Dynamics
  • Fictitious Play and Best Response Dynamic
  • Convergence and Stability: NE and ESS
  • Three-Strategy Game Dynamics
  • Dynamic Stability for General Games
  • Natural Selection at a Single Locus
  • One-Stage Simultaneity Games
  • Multi-armed Bandits
  • Appendix
  • Notes
• Bimatrix Games
  • Nash Equilibria and Strict Equilibrium Sets
  • Bimatrix Replicator and Best Response Dynamics
  • Dynamics for Two-Strategy Bimatrix Games
  • Symmetrized Bimatrix Games
  • Bimatrix Monotone Selection Dynamics
  • Notes
• Asymmetric Games
  • The Normal Form
  • The Extensive Form: NE and ESSets
  • Sets and Agent Normal Forms
  • Dynamics and the Wright Manifold
  • Truly Asymmetric Two-Player Games
  • Truly Symmetric Two-Player Games
  • Asymmetric Games with Two Roles
  • A Hierarchical Hawk-Dove Game
• Natural Selection with Multiple Loci
  • Continuous-Time Selection-Recombination
  • Symmetric Extensive Form with Additive Fitness
  • Recombination
  • Selection and Recombination
  • Notes
• Extensive Form Games
  • N-Player Extensive Form Games
  • Normal Forms and the Replicator Dynamic
  • The Wright Manifold and Replicator Dynamic
  • Symmetric Extensive Form Games
  • Appendix
  • Notes
• Simultaneity Games
  • Elementary Two-Stage Simultaneity Games
  • Two-Stage Two-Strategy Games
  • Asymptotic Stability of Pervasive NE
  • The War of Attrition
  • The Finitely Repeated Prisoner's Dilemma Game
  • Notes
• Perfect Information Games
  • Elementary Perfect Information Games
  • Equilibrium Selection: Dynamic Approach
  • The Centipede Game
  • Extensive Form Bandits
  • Notes
• Subgame Monotonicity
  • Montone Trajectories
  • Subgame Monotone Trajectories
  • An Imitation Example
  • Discussion
  • Notes
• Bibliography

  Index