Rational Adversaries and the Maintenance of Fragility: A Game-Theoretic Theory of Rational Stagnation
Daisuke Hirota
合作制度往往保持在持续不理想但稳定的状态。 本文解释了这种“理性停滞”作为理性对手维持的平衡,其效用遵循潜在损失的原理,u_D = U_ideal - U_actual。 从囚徒困境开始,我们表明变换u_i' = a u_i + b u_j 和相互承认的比例 w = b/a 生成一个脆弱的合作带[w_min, w_max],其中(C,C)和(D,D)都是均衡的。 延伸到具有随机合作回报 R_t 和干预成本(C_c,C_m)的动态模型,贝尔曼式的分析产生了三种战略制度:立即破坏,合理停滞和干预放弃。 附录进一步将效用概括为依赖参考的非线性形式,并证明其在参考变化下的稳定性,确保了框架的稳健性。 对社交媒体算法和政治信任的应用说明了对抗理性如何刻意保持脆弱性。
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...