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We consider a finite structured population of mobile individuals thatstrategically explore a network using a Markov movement model and interact witheach other via a public goods game. We extend the model of Erovenko et al.(2019) from complete, circle, and star graphs to various random networks tofurther investigate the effect of network topology on the evolution ofcooperation. We discover that the network topology affects the outcomes of theevolutionary process only for networks of small average degree. Once the degreebecomes sufficiently high, the outcomes match those for the complete graph. Theactual value of the degree when this happens is much smaller than that of thecomplete graph, and the threshold value depends on other networkcharacteristics.

The evolution of cooperation in a mobile population on random networks: Network topology matters only for low-degree networks