  We introduce a mean-field term to an evolutionary spatial game model. Namely,
we consider the game of Nowak and May, based on the Prisoner's dilemma, and
augment the game rules by a self-consistent mean-field term. This way, an agent
operates based on local information from its neighbors and nonlocal information
via the mean-field coupling. We simulate the model and construct the
steady-state phase diagram, which shows significant new features due to the
mean-field term: while for the game of Nowak and May, steady states are
characterized by a constant mean density of cooperators, the mean-field game
contains steady states with a continuous dependence of the density on the
payoff parameter. Moreover, the mean-field term changes the nature of
transitions from discontinuous jumps in the steady-state density to jumps in
the first derivative. The main effects are observed for stationary steady
states, which are parametrically close to chaotic states: the mean-field
coupling drives such stationary states into spatial chaos. Our approach can be
readily generalized to a broad class of spatial evolutionary games with
deterministic and stochastic decision rules.
