  In the context of Evolutionary Game Theory, one of the most noteworthy
mechanisms to support cooperation is spatial reciprocity, usually accomplished
by distributing players in a spatial structure allowing cooperators to cluster
together and avoid exploitation. This raises an important question: how is the
survival of cooperation affected by different topologies? Here, to address this
question, we explore the Focal Public Goods (FPGG) and classic Public Goods
Games (PGG), and the Prisoner's Dilemma (PD) on several regular lattices:
honeycomb, square (with von Neumann and Moore neighborhoods), kagome,
triangular, cubic, and 4D hypercubic lattices using both analytical methods and
agent-based Monte Carlo simulations. We found that for both Public Goods Games,
a consistent trend appears on all two-dimensional lattices: as the number of
first neighbors increases, cooperation is enhanced. However, this is only
visible by analysing the results in terms of the payoff's synergistic factor
normalized by the number of connections. Besides this, clustered topologies,
i.e., those that allow two connected players to share neighbors, are the most
beneficial to cooperation for the FPGG. The same is not always true for the
classic PGG, where having shared neighbors between connected players may or may
not benefit cooperation. We also provide a reinterpretation of the classic PGG
as a focal game by representing the lattice structure of this category of games
as a single interaction game with longer-ranged, weighted neighborhoods, an
approach valid for any regular lattice topology. Finally, we show that
depending on the payoff parametrization of the PD, there can be an equivalency
between the PD and the FPGG; when the mapping between the two games is
imperfect, the definition of an effective synergy parameter can still be useful
to show their similarities.
