Rational Adversaries and the Maintenance of Fragility: A Game-Theoretic Theory of Rational Stagnation

arXiv:2510.22232v1 Announce Type: cross
Abstract: Cooperative systems often remain in persistently suboptimal yet stable states. This paper explains such “rational stagnation” as an equilibrium sustained by a rational adversary whose utility follows the principle of potential loss, $u_D = U_ideal – U_actual$. Starting from the Prisoner’s Dilemma, we show that the transformation $u_i’ = a,u_i + b,u_j$ and the ratio of mutual recognition $w = b/a$ generate a fragile cooperation band $[w_min,,w_max]$ where both (C,C) and (D,D) are equilibria. Extending to a dynamic model with stochastic cooperative payoffs $R_t$ and intervention costs $(C_c,,C_m)$, a Bellman-style analysis yields three strategic regimes: immediate destruction, rational stagnation, and intervention abandonment. The appendix further generalizes the utility to a reference-dependent nonlinear form and proves its stability under reference shifts, ensuring robustness of the framework. Applications to social-media algorithms and political trust illustrate how adversarial rationality can deliberately preserve fragility.