arXiv Open Access 2025

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

Daisuke Hirota
Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

Penulis (1)

D

Daisuke Hirota

Format Sitasi

Hirota, D. (2025). Rational Adversaries and the Maintenance of Fragility: A Game-Theoretic Theory of Rational Stagnation. https://arxiv.org/abs/2510.22232

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2025
Bahasa
en
Sumber Database
arXiv
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Open Access ✓