Evolutionary Game Theory.

• Author: Ortmann, Andreas

What is evolutionary game theory? It is an attempt to discard the heroic knowledge and rationality assumptions of standard noncooperative (eductive) game theory. It gets its name from the use of evolutionary models which enable us to track the distribution of actions in repeated encounter games. Essentially, evolutionary models are systems of deterministic or stochastic differential or difference equations (dynamical systems), which are derived from the payoff matrix of the same constituent game that eductive game theory takes as point of departure.

Over the past seven or eight years, evolutionary game theory has gained rapid acceptance among game theorists. Its major selling point has been the seeming ability to explain experimental results of repeated encounter games with multiple equilibria.

In his new book, Weibull focuses on continuous evolutionary models of the deterministic variety. For this set of models he offers, often drawing on his own work and that of his collaborators, a well-written, mathematically elegant, and self-contained treatment that has a good chance indeed of becoming a staple of the literature.

The book is divided into six chapters. Chapter One reviews key concepts and results from eductive game theory, such as mixed strategy payoff functions and their geometric interpretation, Nash equilibria, and refinements such as perfection, properness, strict perfection, essentiality, and strategic stability. It also introduces symmetric two-player games which are the main menu of chapters Two through Four, and a nice classification of symmetric 2 x 2 games which is employed throughout the remainder of the text.

Chapter Two discusses evolutionary stability criteria. The notion of an evolutionarily stable strategy (ESS) was at the center of Maynard Smith's exploration of the applicability of game theory to biology [1] and is a refinement of the Nash equilibrium concept, which it augments by a robustness condition that prevents mutants from upsetting the prevailing equilibrium. The ESS is quasi-dynamic in nature, i.e., while it is concerned with evolution, it does not model the evolutionary process explicitly. Chapter Two discusses the ESS and a number of other evolutionary stability criteria (evolutionarily stable sets, equilibrium evolutionarily stable sets); it also offers an intriguing discussion of "cheap talk" (costless pre-play communication) and its ability to produce Pareto efficient outcomes.

Chapters Three and Four...