Work detail

An Introduction to Evolutionary Game Theory

Author: Bc.Vu Phuong Thuy
Year: 2006 - summer
Leaders: doc. PhDr. Martin Gregor Ph.D.
Work type: Bachelors
Language: Czech
Pages: 75
Awards and prizes: B.A. with distinction from the Dean of the Faculty of Social Sciences for an extraordinarily good bachelors diploma thesis
Abstract: The paper discusses the main set of analytical concepts establishing evolutionary game theory with two objectives. Our first objective is to show that evolutionary game theory provides support for Nash equilibrium even if the assumption of perfect rationality is released. Our second objective is to demonstrate the applicability of evolutionary game theory to economic issues.
Evolutionary game theory combines the static concept of Evolutionary Stable Strategy or State with the dynamic concept of replicator dynamics. We start with the static analysis where the ESS concept is presented in contrast with the chief theoretical notion of classical game theory, Nash equilibrium.
We then continue with dynamic analysis, where the equilibrium concept is enriched by the concept of evolutionary focal point. In both analyses we come to the conclusion, that evolutionary equilibrium concepts are refinements of the Nash equilibrium, where the ESS concept is asymptotically stable with respect to the replicator dynamics and thus represents the stricter refinement.
Further, we extend evolutionary stability concepts to the situation of asymmetric games. This case involves two populations, where each population represents an (economically) distinct role.
To demonstrate the applicability of evolutionary game theory to economic issues we then introduce two models of economic interaction. In the first model we interpret d’Artigues and Vignolo (2003)’s model who study the emergence of the recent form of terrorism using evolutionary game theory. The second application deals with the model of Cressman, Morrison a Wen (1998), who examine the economics of crime deterrence from an evolutionary perspective.
The last section is addressed to the areas of application, where in our opinion evolutionary game theory provides us a better insight.
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