  Elucidating the mechanisms that lead to cooperation is still one of the main
scientific challenges of current times, as many common cooperative scenarios
remain elusive and at odds with Darwin's natural selection theory. Here, we
study evolutionary games on populations that are structured beyond pairwise
interactions. Specifically, we introduce a general evolutionary approach that
allows studying situations in which indirect interactions via a neighbor other
than the direct pairwise connection (or via a group of neighbors), impact the
strategy of the focal player. To this end, we consider simplicial graphs that
encode two- and three-body interactions, which enables to study competition
between all possible pairs of social dilemmas and to scrutinize the role of
three-body interactions in all the observed phenomenology. We simultaneously
investigate how social dilemma with different Nash equilibria compete in
simplicial structures and how such a competition is modulated by the unbalance
of 2- and 1-simplices, which in its turn reflects the relative prevalence of
pairwise or group interactions among the players. We report a number of results
that: (i) support that higher-order games allow for non-dominant strategists to
emerge and coexist with dominant ones, a scenario that can't be explained by
any pairwise schemes, no matter the network of contacts; (ii) characterize a
novel transition from dominant defection to dominant cooperation as a function
of the simplicial structure of the population; and (iii) demonstrate that
2-simplex interactions are a source of strategy diversity, i.e. increasing the
relative prevalence of group interactions always promotes diverse strategic
identities of individuals. Our study constitutes a step forward in the quest
for understanding the roots of cooperation and the mechanisms that sustain it
in real-world and social environments.
