Evolution of Cooperation for Multiple Mutant Configurations on All Regular Graphs with $N \leq 14$ players
This provides incremental insights into evolutionary game theory for researchers studying cooperation in network-structured populations.
The paper tackles the problem of understanding how cooperation emerges in structured populations by analyzing all possible arrangements of cooperators and defectors on regular graphs with up to 14 players, showing that the number of graph cycles of certain lengths predicts cooperation tendency and identifying specific structural properties like clusters connected by cut/hinge vertices that promote cooperation.
We study the emergence of cooperation in structured populations with any arrangement of cooperators and defectors on the evolutionary graph. Using structure coefficients defined for configurations describing such arrangements of any number of mutants, we provide results for weak selection to favor cooperation over defection on any regular graph with $N \leq 14$ vertices. Furthermore, the properties of graphs that particularly promote cooperation are analyzed. It is shown that the number of graph cycles of certain length is a good predictor for the values of the structure coefficient, and thus a tendency to favor cooperation. Another property of particularly cooperation-promoting regular graphs with a low degree is that they are structured to have blocks with clusters of mutants that are connected by cut vertices and/or hinge vertices.