Network structure, games, and agent dynamics

Consider a group of agents embedded in a network, repeatedly playing a game with their neighbors. Each agent acts locally but through the links of the network local decisions percolate to the entire population. Past research shows that such a system converges either to an absorbing state (a fixed distribution of actions that once attained does not change) or to an absorbing set (a set of action distributions that may cycle in finite populations or behave chaotically in unbounded populations). In many network games, however, it is uncertain which situation emerges. In this paper I identify two fundamental network characteristics, boundary consistency and neighborhood overlap, that determine the outcome of all symmetric, binary-choice, network games. In quasi-consistent networks these games converge to an absorbing state regardless of the initial distribution of actions, and the degree to which neighborhoods overlap impacts the number and composition of those absorbing states.