Evolutionary Kaleidoscopes

Kaleidoscopes in [math]\displaystyle{ 2\times 2 }[/math] Games

Time evolution of cooperators and defectors in spatially structured populations where individuals interact only within a limited local neighborhood and engage in prisoner's dilemma and snowdrift games.

Color code:	Cooperators	Defectors
	New cooperator	New defector

The following examples illustrate and highlight different relevant and interesting scenarios. All examples are meant as suggestions and starting points for further experiments and explorations of the dynamics of the system.

von Neumann neighborhood ([math]\displaystyle{ k=4 }[/math])

Evolutionary kaleidoscopes in the Prisoner's Dilemma

In the spatial Prisoner's Dilemma cooperators can survive by forming clusters and thereby outweighing losses against defectors along the boundary with interactions within the cluster. For suitable parameters such clusters can expand along straight boundaries but are vulnerable to invasion along rugged boundaries and corners.

For deterministic update rules (synchronous lattice update, best player in neighborhood reproduces) and symmetrical initial configurations this can lead to fascinating spatio-temporal patterns. Such evolutionary kaleidoscopes are certainly only of limited scientific interest but they do have quite some entertainment value.

Evolutionary kaleidoscopes in Snowdrift and Hawk-Dove games

In the spatial Snowdrift or Hawk-Dove game it is favorable to adopt a strategy which opposes the neighboring ones. This leads to smaller and filament like clusters.

As for the Prisoner's Dilemma, determinsitic update rules can again produce fascinating evolutionary kaleidoscopes. Simply by watching the time evolution of the lattice configuration the qualitative difference of the underlying mechanisms become obvious. Given the static pictures to the left, this would be far more difficult to decide.

Kaleidoscopes in Voluntary Public Goods Games

Color code:	Cooperators	Defectors	Loners
	New cooperator	New defector	New loner