One of the joys of philosophy is seeing how things “hang together in the broadest sense” (Sellars, *Philosophy and the Scientific Image of Man,* p.361). Information graphics can be a powerful tool do just this.

Bomze’s Classification of 3×3 Games

Under the Replicator Dynamics

The replicator dynamics is the “first and most important model of evolutionary game theory” (Cressman, *The Replicator Equation and Other Game Dynamics*, p.1081). This dynamics isolate the qualitative influence of selection on evolution, and capture the idea that types that are more fit than the population average fitness grow in proportion, while types that are less fit than average shrink in proportion. When there are three types in a population, there are 49 logical possibilities for the qualitative dynamics of evolution. These dynamics, their stability properties, and relationship to the standard equilibrium concepts (ESS, NSS, ESSet) are captured in this visualization.

Classification of 2×2 Games

Under the Replicator Dynamics

When there are two types in a population, there are 5 logical possibilities for the qualitative dynamics of evolution. These include the famous Prisoner’s Dilemma, Prisoner’s Delight, Stag Hunt, and Hawk-Dove games. In the simple case of two of population composed of types, the ESS concept captures all and only the evolutionarily significant outcomes of the dynamics. These dynamics and their stability properties are captured in this visualization.

Frequency Dependent Moran Process

and the Strong Mutation Condition

The Moran process represents “the simplest possible stochastic model to study selection in a finite population” (Nowak, *Evolutionary Dynamics: Exploring the Equations of Life*, p.94). When there is mutation present, the process is typically analyzed by considering when the mutation rate is very low, the population is very large, or the intensity of selection is very small. These limits can produce different behaviors. I demonstrate an important condition—the strong mutation condition—demarcating an intermediate regime of distinct behavior between these extremes.

[ PDF of Strong Mutation Condition ]