Spatial extensions of evolutionary game theory.

摘要

A simple extension of deterministic evolutionary game dynamics to a spatial model is realized by a grid of simplex-embedded cells, where spatial interaction occurs among range-one von Neumann neighbors of the cells. Spatial Nash equilibrium and spatial ESS are defined, which inherit several properties in common with the classical nonspatial counterparts. At the same time, there exist unique properties which may bear consequences inconsistent with the classical evolutionary game dynamics depending on the degree of spatial interactions. In order to show this, I first introduce the existing knowledge of evolutionary game theory with examples, and apply this concept to a spatial extension.