Directed percolation in higher-order social dilemmas
Villegas, Pablo; Meloni, Sandro
Submitted (2026)
Submitted (2026)
Multiplayer social dilemmas on hypergraphs show a variety of emergent
phenomena, which has been attributed to group interactions. Here we test
whether pairwise dynamics can reproduce them as well. We derive the mesoscopic
Langevin equation of a testbed model and find the operator content of absorbing
phase transitions: a directed-percolation line, a tricritical point, and a
first-order region whose spinodal is the explosive transition. In our analysis,
three-player games only set the values of the Landau coefficients. We construct
a strictly pairwise model with short-lived memory, in which every event
involves at most two entities, that reproduces these coefficients term by term
and has exactly the same mean-field fixed points. Simulations confirm that the
two dynamics share mean-field critical and tricritical scaling and the size of
the critical mass, and that a purely three-player game on a two-dimensional
triangular lattice lies in the directed-percolation class. For these games, the
explosive transition and the critical mass therefore do not require group
interactions, and the critical behavior is that of the pairwise theory.
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