Coevolutionary dynamics of networks and games under birth-death and birth mechanisms

摘要

There is much interest in studying evolutionary games in structured populations, in order to understand how cooperation emerges in communities of egoistic agents. In this paper, we consider a new mechanism for cooperation to survive on networks. Agents are designed to reproduce offspring in proportion to their fitness, i.e., the aggregate payoffs they collected in the previous Prisoner's Dilemma game with neighbours. The population then evolves either by an individual giving birth to an offspring that takes over a random neighbour (birth-death process dynamics as the competition for resources already occupied by others) or by an individual constructing one new site from unexploited resources for its offspring (birth process dynamics as the competition for the unexploited resources which induces the extension of system). The underlying interaction network thus evolves and expands simultaneously with the population dynamics. The birth process dynamics is proved to be one new route that favours cooperators, under which cooperators can successfully resist the invasion of defectors in spite of large cost. Furthermore, under this "birth-death & birth" mechanism, the resulting network has a scale-free degree distribution, a small-world property, and hierarchical topology.