We study the evolution of cooperation in the prisoner's dilemma game on time-invariant heterogeneous payoff landscapes on regular and heterogeneous networks. Correlations in the landscape structure and their implications for the evolution of cooperation are investigated. On regular networks we find that negatively and neutrally correlated payoff landscapes strongly enhance cooperation, while positively correlated landscapes may suppress the evolution of cooperation. On heterogeneous networks, cooperation is facilitated if payoff stochasticity is positively correlated with network heterogeneity and may be suppressed otherwise.

We investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected old nodes. In between node additions, the network is rewired to minimize its path length. For time scales at which neither the assembly nor the optimization processes are dominant, we find a rich variety of complex networks with power law tails in the degree distributions. These networks also exhibit nontrivial clustering, a hierarchical organization, and interesting degree-mixing patterns.