  We consider a network of coupled agents playing the Prisoner's Dilemma game,
in which players are allowed to pick a strategy in the interval [0,1], with 0
corresponding to defection, 1 to cooperation, and intermediate values
representing mixed strategies in which each player may act as a cooperator or a
defector over a large number of interactions with a certain probability. Our
model is payoff-driven, i.e., we assume that the level of accumulated payoff at
each node is a relevant parameter in the selection of strategies. Also, we
consider that each player chooses his/her strategy in a context of limited
information. We present a deterministic nonlinear model for the evolution of
strategies. We show that the final strategies depend on the network structure
and on the choice of the parameters of the game. We find that polarized
strategies (pure cooperator/defector states) typically emerge when (i) the
network connections are sparse, (ii) the network degree distribution is
heterogeneous, (iii) the network is assortative, and surprisingly, (iv) the
benefit of cooperation is high.
