From Two Players to a Galactic Network: Entry, Extinction, Coalitions, Cliques and Spatial Topology in Interstellar Strategic Interaction

Abstract

Dark Forest arguments commonly reduce interstellar strategy to a bilateral encounter between two persistent civilisations. A galaxy, however, is an open population in which civilisations enter, disappear, form selective relationships and occupy a spatially constrained network. This paper develops a continuous-time Galactic Network Formation Game integrating demographic turnover, endogenous trust links, directed hostile reach, coalition formation, causal delay and extinction cascades. Civilisations arise at vacant sites and disappear through baseline, predatory and coordination hazards. Pairwise-stable trust links possess an exact distance threshold expressed with the Lambert W function. In a homogeneous three-dimensional field, the model derives a critical entry rate for formation of a giant trusted component. Coalition governance is constrained by a causal-diameter bound, which can make several galactic cliques necessary even when a topological giant component exists. A congestion-security payoff yields conditions for a unique locally stable coalition size. Coalition survival under random or targeted extinction is represented by core pruning, with closed mean-field equations for cascade size. Numerical illustrations reveal sparse archipelagos, brittle cliques, resilient cliques and temporally admissible federations. Cosmic silence, cooperation and pre-emption are therefore network-level outcomes rather than universal consequences of uncertainty.