  We consider a finite structured population of mobile individuals that
strategically explore a network using a Markov movement model and interact with
each 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 to
further investigate the effect of network topology on the evolution of
cooperation. We discover that the network topology affects the outcomes of the
evolutionary process only for networks of small average degree. Once the degree
becomes sufficiently high, the outcomes match those for the complete graph. The
actual value of the degree when this happens is much smaller than that of the
complete graph, and the threshold value depends on other network
characteristics.
