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

• URL: http://arxiv.org/abs/2510.22232v1
• Date: Sat, 25 Oct 2025 09:28:15 GMT
• Title: Rational Adversaries and the Maintenance of Fragility: A Game-Theoretic Theory of Rational Stagnation
• Authors: Daisuke Hirota,
• Abstract summary: This paper explains such "rational stagnation" as an equilibrium sustained by a rational adversary.<n> Applications to social-media algorithms and political trust illustrate how adversarial can deliberately preserve rationality.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Body-Reservoir Governance in Repeated Games: Embodied Decision-Making, Dynamic Sentinel Adaptation, and Complexity-Regularized Optimization [0.0]
  We propose a three-layer Body-Reservoir Governance architecture.<n> Strategy complexity cost is defined as the KL divergence between the reservoir's state distribution and its habituated baseline.<n>Body governance reduces this cost, with action variance decreasing up to $1600times$ with dimension $d$.<n>Overriding the body incurs thermodynamic cost proportional to internal state distortion.
  arXiv  Detail & Related papers  (2026-02-24T12:36:41Z)
• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• Mutual Information Collapse Explains Disentanglement Failure in $β$-VAEs [4.155522769716163]
  $$-VAE is a framework for unsupervised disentanglement.<n> benchmarks such as MIG and SAP typically peak at intermediate $$ and collapse as regularization increases.<n>We introduce the $$-VAE, which decouples regularization pressure from informational collapse.
  arXiv  Detail & Related papers  (2026-02-09T23:38:11Z)
• Stabilizing Fixed-Point Iteration for Markov Chain Poisson Equations [49.702772230127465]
  We study finite-state Markov chains with $n$ states and transition matrix $P$.<n>We show that all non-decaying modes are captured by a real peripheral invariant subspace $mathcalK(P)$, and that the induced operator on the quotient space $mathbbRn/mathcalK(P) is strictly contractive, yielding a unique quotient solution.
  arXiv  Detail & Related papers  (2026-01-31T02:57:01Z)
• Phase Transition for Budgeted Multi-Agent Synergy [41.486076708302456]
  Multi-agent systems can improve reliability, yet under a fixed inference budget they often help, saturate, or even collapse.<n>We develop a minimal and calibratable theory that predicts these regimes from three binding constraints of modern agent stacks.
  arXiv  Detail & Related papers  (2026-01-24T05:32:50Z)
• Blind Inverse Game Theory: Jointly Decoding Rewards and Rationality in Entropy-Regularized Competitive Games [0.0]
  We introduce Blind-IGT, the first statistical framework to jointly recover $theta$ and $tau$ from observed behavior.<n>We prove it achieves the optimal $mathcalO(N-1/2)$ convergence rate for joint parameter recovery.<n>We extend our framework to Markov games and demonstrate optimal convergence rates with strong empirical performance.
  arXiv  Detail & Related papers  (2025-11-07T16:27:59Z)
• Probabilistically stable revision and comparative probability: a representation theorem and applications [0.0]
  We show that a selection function can be representable as a strong-stable-set operator on a finite probability space.<n>The resulting logic of probabilistically stable belief revision exhibits strong monotonicity properties.<n>We point out two applications of our main result to the theory of simple voting games and to revealed preference theory.
  arXiv  Detail & Related papers  (2025-09-02T16:42:47Z)
• Prediction-Augmented Mechanism Design for Weighted Facility Location [1.6552489352816389]
  We provide a prediction augmented algorithmic framework for balancing the consistency and robustness over strategic agents with non-uniform weights.<n>We prove that there is no strategyproof deterministic mechanism that reach $1$-consistency and $Oleft( n cdot fracW_maxW_min right)$-robustness in weighted FLP, even with fully predictions of all agents.
  arXiv  Detail & Related papers  (2025-07-09T03:13:52Z)
• Simple Convergence Proof of Adam From a Sign-like Descent Perspective [58.89890024903816]
  We show that Adam achieves the optimal rate of $cal O(frac1Ts14)$ rather than the previous $cal O(fracln TTs14)$.<n>Our theoretical analysis provides new insights into the role of momentum as a key factor ensuring convergence.
  arXiv  Detail & Related papers  (2025-07-08T13:19:26Z)
• Institutional Noise, Strategic Deviation, and Intertemporal Collapse: A Formal Model of Miner Behaviour under Protocol Uncertainty [0.0]
  This paper develops a formal game-theoretic model to examine how protocol mutability disrupts cooperative mining behaviour in blockchain systems.<n>Using a repeated game framework with rule shocks, we show that even minor uncertainty in institutional rules increases time preference and induces strategic deviation.<n>We conclude that protocol design must be treated as a constitutional economic constraint, not a discretionary variable, if sustainable cooperation is to emerge in decentralised systems.
  arXiv  Detail & Related papers  (2025-06-26T04:12:06Z)
• Towards a Sharp Analysis of Offline Policy Learning for $f$-Divergence-Regularized Contextual Bandits [49.96531901205305]
  We analyze $f$-divergence-regularized offline policy learning.<n>For reverse Kullback-Leibler (KL) divergence, we give the first $tildeO(epsilon-1)$ sample complexity under single-policy concentrability.<n>We extend our analysis to dueling bandits, and we believe these results take a significant step toward a comprehensive understanding of $f$-divergence-regularized policy learning.
  arXiv  Detail & Related papers  (2025-02-09T22:14:45Z)
• Collaborative Mean Estimation Among Heterogeneous Strategic Agents: Individual Rationality, Fairness, and Truthful Contribution [11.371461065112422]
  We study a collaborative learning problem where $m$ agents aim to estimate a vector $mu =(mu_k, sigma2)_kin[d]$.<n>Instead of working independently, agents can exchange data, collecting cheaper samples and sharing them in return for costly data, thereby reducing both costs and estimation error.
  arXiv  Detail & Related papers  (2024-07-20T17:45:40Z)
• Sequential Manipulation Against Rank Aggregation: Theory and Algorithm [119.57122943187086]
  We leverage an online attack on the vulnerable data collection process. From the game-theoretic perspective, the confrontation scenario is formulated as a distributionally robust game. The proposed method manipulates the results of rank aggregation methods in a sequential manner.
  arXiv  Detail & Related papers  (2024-07-02T03:31:21Z)
• A Robustness Analysis of Blind Source Separation [91.3755431537592]
  Blind source separation (BSS) aims to recover an unobserved signal from its mixture $X=f(S)$ under the condition that the transformation $f$ is invertible but unknown. We present a general framework for analysing such violations and quantifying their impact on the blind recovery of $S$ from $X$. We show that a generic BSS-solution in response to general deviations from its defining structural assumptions can be profitably analysed in the form of explicit continuity guarantees.
  arXiv  Detail & Related papers  (2023-03-17T16:30:51Z)
• Toward Adversarial Robustness via Semi-supervised Robust Training [93.36310070269643]
  Adrial examples have been shown to be the severe threat to deep neural networks (DNNs) We propose a novel defense method, the robust training (RT), by jointly minimizing two separated risks ($R_stand$ and $R_rob$)
  arXiv  Detail & Related papers  (2020-03-16T02:14:08Z)
• Distributional Robustness and Regularization in Reinforcement Learning [62.23012916708608]
  We introduce a new regularizer for empirical value functions and show that it lower bounds the Wasserstein distributionally robust value function. It suggests using regularization as a practical tool for dealing with $textitexternal uncertainty$ in reinforcement learning.
  arXiv  Detail & Related papers  (2020-03-05T19:56:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.