聚合博弈的隐私与真实均衡选择
Privacy and Truthful Equilibrium Selection for Aggregative Games
摘要：
我们研究一类非常普遍的游戏-多维聚合游戏-特别是推广匿名游戏和加权拥塞游戏。对于任何这样的游戏，也是大的，我们解决了均衡选择问题在很强的意义。特别地，我们给出了一个有效的弱中介：一个只具有倾听报告类型和提供无约束力的建议行动的能力的机制，使得（a）每个局中人如实地向中介报告他们的类型，然后遵循其建议行动是一个渐近纳什均衡;（b）当局中人这样做时，他们最终会在诱导完全信息博弈的一个特定的渐近纯策略纳什均衡上协调。事实上，真实的报告是中介博弈的事后纳什均衡，因此我们的解决方案即使在信息不完整的情况下也适用，即使参与者类型是任意的或最坏的情况（即不是从共同的先验中得出的）。我们实现了这一点，给出了一个有效的差分私人算法计算纳什均衡在这样的游戏。所有结果的收敛速度都是关于参与人个数的逆多项式$n$。我们还将我们的主要结果应用到多维市场博弈中。我们的结果可以被看作是给，丰富的游戏类，一个更强大的版本的启示原则，在我们的工作与较弱的信息假设（没有共同的先验），但提供了一个更强的解决方案的概念（事后纳什与贝叶斯纳什均衡）。与之前的工作相比，我们的主要概念贡献是表明弱介体是存在于各种游戏中的博弈论对象-以前，它们只存在于交通路由游戏中。
英文摘要：
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.
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