  In this work we study the behavior of classical two-person, two-strategies
evolutionary games on networks embedded in a Euclidean two-dimensional space
with different kinds of degree distributions and topologies going from regular
to random, and to scale-free ones. Using several imitative microscopic
dynamics, we study the evolution of global cooperation on the above network
classes and find that specific topologies having a hierarchical structure and
an inhomogeneous degree distribution, such as Apollonian and grid-based
networks, are very conducive to cooperation. Spatial scale-free networks are
still good for cooperation but to a lesser degree. Both classes of networks
enhance average cooperation in all games with respect to standard random
geometric graphs and regular grids by shifting the boundaries between
cooperative and defective regions. These findings might be useful in the design
of interaction structures that maintain cooperation when the agents are
constrained to live in physical two-dimensional space.
