{"ID":2850269,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22232","arxiv_id":"2510.22232","title":"Rational Adversaries and the Maintenance of Fragility: A Game-Theoretic Theory of Rational Stagnation","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.","short_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 th...","url_abs":"https://arxiv.org/abs/2510.22232","url_pdf":"https://arxiv.org/pdf/2510.22232v1","authors":"[\"Daisuke Hirota\"]","published":"2025-10-25T09:28:15Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"cs.AI\",\"econ.TH\"]","methods":"[\"Large Language Model\"]","has_code":false}