Evolutionary Dynamics and Extensive Form Games

Abstract

An analysis of standard evolutionary dynamics adapted to 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.

Working Well with Others: The Evolution of Teamwork and Ethics

“…Instead, the northwest cell represents the outcome when a shirker is monitored, the southwest cell a shirker-nonmonitor encounter, etc. The underlying game may indeed be in extensive form (Cressman, 2003).…”

Partner Selection Shapes the Strategic and Topological Evolution of Cooperation

“…Evolutionary game theory provides a simple yet effective framework for investigating this issue [2][3][4][5][6][7][8]. As a mathematical metaphor, the Prisoner's Dilemma game is capable of capturing the essence of cooperation problems in the real world [9].…”

Lyapunov Functions for Time-Scale Dynamics on Riemannian Geometries of the Simplex

“…This equation is trajectory equivalent to the replicator equation (up to a change in velocity and transformation of f (x) so thatf (x) > 0) [9,19]. The definitions of the time-scale calculus can unify the description of continuous and discrete dynamics in evolutionary dynamics, as well as set the stage for dynamics on other time-scales, through the delta derivative.…”

“…Ultimately we define the time-scale escort incentive dynamic and time-scale metric dynamics (which in the continuous case correspond to a special case of the adaptive dynamics of [18]), building up through a series of examples, and prove a general stability theorem for a large class of discrete and continuous dynamics. For general introductions to evolutionary dynamics see [9,19,20].…”