Relationships between dilemma strength and fixation properties in coevolutionary games

Whether or not cooperation is favored over defection in evolutionary games can be assigned by structure coefficients for any arrangement of cooperators and defectors on any network modeled as a regular graph. We study how these structure coefficients relate to a scaling of dilemma strength in social dilemma games. It is shown that some graphs permit certain arrangements of cooperators and defectors to possess particularly large structure coefficients. Moreover, these large coefficients imply particularly large sections of a bounded parameter plane spanned by scaling gamble-intending and risk-averting dilemma strength

Evolution of Cooperation for Multiple Mutant Configurations on All Regular Graphs with N≤14N \leq 14 players

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