Evolution of Cooperation for Multiple Mutant Configurations on All Regular Graphs with N ? 14 Players

Hendrik Richter
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Hendrik Richter: Faculty of Engineering, HTWK Leipzig University of Applied Sciences, D-04251 Leipzig, Germany

Games, 2020, vol. 11, issue 1, 1-18

Abstract: We study the emergence of cooperation in structured populations with any arrangement of cooperators and defectors on the evolutionary graph. In a computational approach 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 ≤ 14 vertices. Furthermore, the properties of graphs that particularly promote cooperation are analyzed. It is shown that the number of graph cycles of a 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.

Keywords: evolutionary game theory; fixation properties; structure coefficients; regular graphs; graph–theoretical properties; graph cycles (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2020
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