Strategic reasoning for socially good mechanisms

The design and evaluation of mechanisms for aggregating preferences is a central problem in Multi-Agent Systems (MAS). In such setting, we need to be able to aggregate individual preferences, which are conflicting when agents are self-interested. More importantly, the mechanism should choose a socially desirable (or ""good"") outcome and reach an equilibrium despite the fact that agents can lie about their preferences. The real-world applications of designing and verifying mechanisms for social choice are manifold, including fair division protocols, secure voting, and truth-tracking via approval voting. Although logic-based languages have been widely used for verification and synthesis of MAS, the use of formal methods for reasoning about auctions under strategic behavior as well as automated mechanism design has not been much explored yet. An advantage in adopting such perspective lies in the high expressivity and generality of logics for strategic reasoning. Moreover, by relying on precise semantics, formal methods provide tools for rigorously analyzing the correctness of systems, which is important to improve trust in mechanisms generated by machines. This project aims to design a logical framework based on Strategy Logic (SL) for formally verifying and designing mechanisms for social choice. More specifically, we aim at (i) proposing an approach addressing the probabilistic setting (with Bayesian information, stochastic transitions and mixed strategies)