[论文解读] Privacy and Truthful Equilibrium Selection for Aggregative Games

Rachel Cummings, Michael Kearns+2 more|arXiv (Cornell University)|Jul 29, 2014

Auction Theory and Applications参考文献 18被引用 13

一句话总结

本文提出了一种用于大规模多维聚合博弈的差分隐私弱中立机制，确保真实报告并协调至纯策略纳什均衡。其通过使用隐私保护算法计算近似纳什均衡，实现了一种事后的纳什均衡，即使在无共同先验或对玩家类型无分布假设的情况下，也能激励诚实报告。

ABSTRACT

We study a very general class of games --- multi-dimensional aggregative games --- which in particular generalize both anonymous games and weighted congestion games. For any such game that is also large, we solve the equilibrium selection problem in a strong sense. In particular, we give an efficient weak mediator: a mechanism which has only the power to listen to reported types and provide non-binding suggested actions, such that (a) it is an asymptotic Nash equilibrium for every player to truthfully report their type to the mediator, and then follow its suggested action; and (b) that when players do so, they end up coordinating on a particular asymptotic pure strategy Nash equilibrium of the induced complete information game. In fact, truthful reporting is an ex-post Nash equilibrium of the mediated game, so our solution applies even in settings of incomplete information, and even when player types are arbitrary or worst-case (i.e. not drawn from a common prior). We achieve this by giving an efficient differentially private algorithm for computing a Nash equilibrium in such games. The rates of convergence to equilibrium in all of our results are inverse polynomial in the number of players $n$. We also apply our main results to a multi-dimensional market game. Our results can be viewed as giving, for a rich class of games, a more robust version of the Revelation Principle, in that we work with weaker informational assumptions (no common prior), yet provide a stronger solution concept (ex-post Nash versus Bayes Nash equilibrium). In comparison to previous work, our main conceptual contribution is showing that weak mediators are a game theoretic object that exist in a wide variety of games -- previously, they were only known to exist in traffic routing games.

研究动机与目标

• 解决玩家信息不完全且存在多个纳什均衡的大规模聚合博弈中的均衡选择问题。
• 设计一种弱中立机制，激励玩家真实报告类型，并在无需共同先验的情况下协调至特定纳什均衡。
• 将弱中立机制的适用范围从交通路由博弈扩展至更广泛的博弈类别，包括匿名博弈和加权冲突博弈。
• 通过利用线性目标函数，优化纳什均衡以改善最坏情况下的结果。
• 提供对揭示原理的稳健替代方案，实现在无贝叶斯假设下达到事后的纳什均衡。

提出的方法

• 使用差分隐私算法 PSummNash，在保护玩家隐私的同时计算大规模聚合博弈中的纳什均衡。
• 采用稀疏机制，以对数误差随查询数量增长的方式，高效回答关于玩家最优响应和聚合函数的大量查询。
• 应用三组查询以检测最优响应函数的近似不动点、检测策略组合的不连续性，并验证均衡条件。
• 通过在策略组合上构建“平滑路径”，通过连续评估扰动后的策略组合来识别稳定均衡。
• 通过联合差分隐私实现隐私保障，确保无法从中介输出中推断出单个玩家的数据。
• 采用两阶段算法：首先通过不动点近似识别候选均衡，然后通过连续策略组合评估进行优化。

实验结果

研究问题

• RQ1 能否构建一种弱中立机制，使得在不假设共同先验的情况下，确保在大规模聚合博弈中实现真实报告与均衡协调？
• RQ2 能否设计一种此类中立机制，以计算优化线性目标函数的纳什均衡，而非最坏情况下的均衡？
• RQ3 是否可能将弱中立机制的存在性从交通路由博弈扩展至更广泛的博弈类别，包括匿名博弈和加权冲突博弈？
• RQ4 如何利用差分隐私确保在均衡选择中同时实现隐私保护与战略激励？
• RQ5 在最坏情况或任意玩家类型设定下，该中立机制能否实现事后的纳什均衡特性？

主要发现

• 所提出的 PSummNash 算法满足 ε-联合差分隐私，并以至少 1−β 的概率计算出 (10α + 2γ)-近似纯策略纳什均衡。
• 收敛至均衡的速度与玩家数量 n 的多项式倒数成正比，确保在大规模博弈中的可扩展性。
• 即使玩家类型为任意或最坏情况，真实报告并遵循中立机制建议仍构成事后的纳什均衡。
• 该方法成功将弱中立机制扩展至多维聚合博弈，其涵盖的博弈类别显著广于以往（例如，此前仅限于交通路由博弈）。
• 该算法是首个实现弱中立机制并优化线性目标函数的算法，而非选择任意或最坏情况下的纳什均衡。
• 研究结果提供了一种稳健的揭示原理替代方案，无需共同先验，且实现了更强的事后均衡激励。