Mechanism Design (MD) aims at defining resources allocation protocols that satisfy a predefined set of properties, and Auction Mechanisms are of foremost importance. Core properties of mechanisms, such as strategy-proofness or budget balance, involve: (i) complex strategic concepts such as Nash equilibria, (ii) quantitative aspects such as utilities, and often (iii) imperfect information, with agents' private valuations. We demonstrate that Strategy Logic provides a formal framework fit to model mechanisms and express such properties, and we show that it can be used either to automatically check that a given mechanism satisfies some property (verification), or automatically produce a mechanism that does (synthesis). To do so, we consider a quantitative and variant of Strategy Logic. We first show how to express the implementation of social choice functions. Second, we show how fundamental mechanism properties can be expressed as logical formulas, and thus evaluated by model checking. We then prove that model checking for this particular variant of Strategy Logic can be done in polynomial space. Next, we show how MD can be rephrased as a synthesis problem, where mechanisms are automatically synthesized from a partial or complete logical specification. We solve the automated synthesis of mechanisms in two cases: when the number of actions is bounded, and when agents play in turns. Finally, we provide examples of auction design based for each of these two cases. The benefit of our approach in relation to classical MD is to provide a general framework for addressing a large spectrum of MD problems, which is not tailored to a particular setting or problem.

中文翻译：

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社会选择机制的形式验证和综合


机制设计 （MD） 旨在定义满足一组预定义属性的资源分配协议，而拍卖机制是最重要的。机制的核心属性，如策略证明或预算平衡，涉及：（i） 复杂的战略概念，如纳什均衡，（ii） 定量方面，如效用，通常 （iii） 信息不完善，与代理人的私人估值。我们证明了 Strategy Logic 提供了一个适合建模机制和表达这些属性的形式框架，并且我们表明它既可以用于自动检查给定机制是否满足某些属性（验证），也可以自动生成满足某些属性的机制（综合）。为此，我们考虑 Strategy Logic 的 quantitative 和 variant。我们首先展示如何表达社会选择函数的实现。其次，我们展示了如何将基本机制属性表示为逻辑公式，从而通过模型检查进行评估。然后，我们证明 Strategy Logic 的这个特定变体的模型检查可以在多项式空间中完成。接下来，我们展示了如何将 MD 改写为综合问题，其中机制是从部分或完整的逻辑规范自动综合的。我们在两种情况下解决了机制的自动合成：当动作数量受到限制时，以及当代理轮流播放时。最后，我们提供了针对这两种情况的拍卖设计示例。相对于经典 MD，我们的方法的好处是提供了一个通用框架来解决大量的 MD 问题，这些问题不是针对特定环境或问题量身定制的。