Directed percolation in higher-order social dilemmas

Abstract

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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BibTeX RIS

BibTeX

@misc{villegas2026directed,
  title = {{Directed percolation in higher-order social dilemmas}},
  author = {Pablo Villegas and Sandro Meloni},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18506},
  eprint = {2610.18506},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18506},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Directed percolation in higher-order social dilemmas
AU  - Pablo Villegas
AU  - Sandro Meloni
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18506
UR  - https://arxiv.org/abs/2610.18506
AB  - 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.
ER  -

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