  We analyze the influence of multiplayer interactions and network adaptation
on the stability of equilibrium points in evolutionary games. We consider the
Snowdrift game with both two-player and three-player interactions on simplicial
complexes. The state of the system and the topology of the interactions are
both adaptive through best response strategies of nodes and rewiring strategies
of edges, respectively. We derive a closed set of low-dimensional differential
equations using pairwise moment closure, which yields an approximation of the
lower moments of the system. We numerically confirm the validity of these
moment equations. Moreover, we demonstrate that the stability of the fixed
points remains unchanged for the considered adaption process. This stability
result indicates that rational best response strategies in games are very
difficult to destabilize, even if higher-order interactions are taken into
account.
