可计算但不可学习的无信息价值均衡与算法合谋的监管
The Computable but Not Learnable Information-Value-Free Equilibria and Regulation of Algorithmic Collusion
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中文总结 AI 辅助
该研究指出无信息价值均衡可高效离线计算但无法被广泛学习算法学习，其结果对算法合谋监管及学习算法收敛至纳什均衡的信息论不可能性具有重要意义。
中文摘要 AI 辅助
无信息价值的相关均衡是指，当所有其他玩家遵循各自的均衡策略时，每个玩家都存在一个行动，其收益与自身均衡策略的收益相同；可学习均衡则是指，仅使用每个玩家自身收益的全反馈的特定学习算法生成的博弈经验历史会收敛至该均衡。我们的主要结果是，尽管无信息价值均衡可在离线场景中高效计算，但它无法被广泛类别的学习算法学习到，这种可计算性与可学习性的分离与经典均衡概念形成鲜明对比，经典均衡概念中离线计算与在线学习的难度通常相当。从信息经济学角度看，我们的结果意味着博弈中相关均衡的学习无法避免产生有价值的信息，这对当前关于算法合谋监管的讨论具有重要意义：在可理性化学习下，有价值的隐性信息交换不可避免，因此传统针对此类交换的反垄断监管与可理性化学习不兼容；此外，我们的结果还为广泛类别的学习算法以时间平均收敛至纳什均衡提供了一种信息论层面的不可能性结果。
英文摘要
A correlated equilibrium is information-value-free if every player has an action that yields the same payoff as their equilibrium strategy when all other players follow their respective equilibrium strategies. An equilibrium is learnable if the empirical history of play generated by certain learning algorithms using only full feedback on each player's own payoff converges to it. Our main result is that although an information-value-free equilibrium can be computed efficiently offline, it is not learnable by a broad class of learning algorithms. This separation stands in sharp contrast to canonical equilibrium concepts, where offline computation and online learning typically have comparable difficulty. In information-economics terms, our results imply that learning correlated equilibria in games cannot avoid generating valuable information, which has implications for current debates on the regulation of algorithmic collusion: Valuable and implicit information exchange is unavoidable under rationalizable learning, and traditional antitrust regulation against such exchange is therefore incompatible with rationalizable learning. Our results also imply an informational impossibility result for time-average convergence to a Nash equilibrium by a broad class of learning algorithms.
