Simplex Plots

In an n-player game with three types or strategies, it is possible to graph "evolutionary trajectories" using replicator dynamics, but this requires a 'simplex': an equilateral triangle in which each point represents a combination of three proportions that sum up to one. The vertices are the points at which 100% of the players choose a given strategy. An example is adding a "Bourgeois" strategy that plays hawk if "home", dove if "away" to the classic Hawk-Dove game:

Using replicator dynamics, we can then evaluate for any given proportion of types where the evolutionary trajectory leads us - and represent this in the simplex using arrows:



Making these graphs "by hand" is way too painful. Luckily Richard McElreath at UC Davis wrote an r-package called baryplot which lets you make simplex plots very easily. It only requires specifying the payoffs for each strategy and starting points for the arrows.