算法合谋与信息价值无关均衡的复杂性
Algorithmic Collusion and the Complexity of Information-Value-Free Equilibria
- Carnegie Mellon University（卡内基梅隆大学）
- Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究信息价值无关均衡的计算复杂性，证明IVFCE在简洁博弈中为PPAD完全且无高效学习动态，而IVFCCE的近似计算虽可FPTAS但指数小近似下至少与P矩阵LCP一样难。
AI中文摘要：
（粗）相关均衡（CE）被称为信息价值无关的（IVF），如果玩家可以通过承诺采取固定行动来匹配从建议中获得的收益。出于监管算法合谋问题的动机，这一精化概念由Hartline、Wang和Zhang [EC'26]提出，他们证明了在显式表示的正则形式博弈中可以在多项式时间内计算。在本文中，我们研究了简洁博弈中IVF(C)CEs的复杂性，这些博弈模拟了更具现实性的战略互动，其特征是玩家众多或纯策略数量指数级增长。我们首先证明，在许多玩家的多矩阵博弈或双人贝叶斯博弈中，即使近似为常数，计算信息价值无关的CE也是PPAD完全的。我们还证明了无条件指数查询下界。我们的结果表明，即使在集中式模型中，IVFCEs也是难以处理的，并排除了任何高效学习动态的存在。这显著加强了Hartline、Wang和Zhang的不可能性结果（该结果涉及特定类别的学习算法），并为近期关于算法合谋的监管提供了强有力的计算批评。为了规避这些困难结果，我们研究了信息价值无关的CCE的复杂性。某些无遗憾算法——如遗憾匹配或FTRL——为该问题提供了完全多项式时间近似方案（FPTAS）。当近似指数级小时，复杂性变得微妙。一方面，利用无遗憾动态，我们确立了在$\text{CLS} = \text{PPAD} \cap \text{PLS}$中的成员资格。另一方面，我们证明它至少与P矩阵线性互补问题一样困难，因此与简单随机博弈一样困难。这表明，除非有重大突破，否则即使是IVFCCEs也不太可能有多项式时间算法。
英文摘要：
A (coarse) correlated equilibrium (CE) is information-value-free (IVF) if a player can match the payoff obtained from recommendations by committing to a fixed action. Motivated by the problem of regulating algorithmic collusion, this refinement was introduced by Hartline, Wang, and Zhang [EC'26], who showed that it can be computed in polynomial time in explicitly represented normal-form game. In this paper, we examine the complexity of IVF(C)CEs in succinct games, which model more realistic strategic interactions that feature either many players or exponentially many pure strategies. We first show that computing an information-value-free CE is PPAD-complete in many-player polymatrix games or two-player Bayesian games, even when the approximation is a constant. We also prove an unconditional exponential query lower bound. Our results establish that IVFCEs are intractable, even in the centralized model, and rule out the existence of any efficient learning dynamics. This significantly strengthens the impossibility result of Hartline, Wang, and Zhang, which concerns a particular class of learning algorithms, and furnishes strong computational critiques of recent regulation on algorithmic collusion. To sidestep these hardness results, we examine the complexity of information-value-free CCE. Certain no-regret algorithms---such as regret matching or FTRL---provide a fully polynomial-time approximation scheme (FPTAS) for this problem. The complexity when the approximation is exponentially small turns out to be nuanced. On the one hand, leveraging no-regret dynamics, we establish membership in $\text{CLS} = \text{PPAD} \cap \text{PLS}$. On the other hand, we show that it is at least as hard as the P-matrix linear complementarity problem, and hence as hard as simple stochastic games. This shows that even IVFCCEs are unlikely to admit a polynomial-time algorithm barring a major breakthrough.
