Explosive Radicalization, Hysteresis, and Peer Punishment on Hypergraphs: An Evolutionary Hawk–Dove Game Approach to Cancel Culture

In contemporary online social environments, the dynamics of the attention economy drive moral outrage and payoff-seeking diffusion, resulting in sudden collective ostracism and cancel culture. Extending recent adaptive network models of incomplete information games and the market for lemons, this study formulates an evolutionary Hawk–Dove game on simplicial complexes (hypergraphs) to capture multi-body collective interactions. We incorporate a nonlinear subjective payoff function parameterized by algorithmic boost and macro-level attention trends into 2-simplex group interactions. Both rigorous analytical derivations via higher-order replicator equations and large-scale tensor-based multi-agent simulations (N=102 to 5×104) reveal that group interactions induce a saddle-node bifurcation, triggering a discontinuous (first-order) phase transition toward explosive radicalization. Furthermore, we computationally prove that cancel culture dynamics exhibit strong collective hysteresis: post hoc cooling-off interventions fail to restore the system to baseline informational integrity due to an irreversible relaxation trap. Finally, by evaluating decentralized sanctions (peer punishment), we identify a sharp critical boundary (αpunish≈0.3) governed by punishment penalty rather than execution cost. Through novel sensitivity analysis, we demonstrate that this threshold is scale-free and remarkably invariant to algorithmic boost levels. Below this threshold, second-order free-riding causes systemic breakdown, whereas sufficient punishment establishes an absolute absorbing state of informational integrity. These findings establish optimal architectural prerequisites for next-generation platform governance.