Rational Adversaries and the Maintenance of Fragility: A Game-Theoretic Theory of Rational Stagnation
Daisuke Hirota
TL;DR
The paper studies why cooperative systems can remain in persistently suboptimal states by introducing a rational adversary whose utility equals the gap between an ideal cooperative outcome and the actual outcome, $u_{D}=U_{ideal}-U_{actual}$. It builds a dynamic, Bellman-style model in which cooperative payoffs $R_t$ are stochastic and intervention costs exist, yielding three strategic regimes: immediate destruction, rational stagnation, and intervention abandonment; the model introduces a fragile cooperation band with thresholds $w_{min}$ and $w_{max}$ tied to payoff parameters via $w_{min}=(T-R)/(R-S)$ and $w_{max}=(P-S)/(T-P)$. The analysis further extends to nonlinear, reference-dependent utilities and proves stability under reference shifts, and the authors illustrate applications to social-media algorithms and political trust, highlighting how adversarial rationality can deliberately preserve fragility while potentially growing latent value. By reframing stagnation as a rationally maintained equilibrium and proposing adversarial mechanism design, the work offers a principled lens for understanding and mitigating fragility in AI systems and institutions.
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.