Numerous problems in the sharing-economy platforms (such as Uber, Airbnb, and TaskRabbit) and virtual power plants (such as Tesla Virtual Power Plant in the US and Next Kraftwerke in Europe), can be modeled as multi-agent systems, when suitably generalizing the deterministic discrete-event systems. In the past decade, many such platforms have been deployed at scale, there has been substantial progress in modeling stochastic systems, and there is much interest in regulating such platforms (cf. renewable energy communities and citizen energy communities in the Renewable Energy Directive and the Internal Electricity Market Directive, or the The Digital Markets Act in the EU). According to some opinions, this will yield a new wave of interest in multi-agent systems. Many novel, fundamental questions arise in connection with the deployment of such generalized multi-agent systems in the sharing economy and beyond, which are not only providing decision support, but actually execute actions (“perform actuation”). First, the participants have only partial information about the system and are not perfectly rational.This is well understood in behavioral economics, but has not been considered in many calculi in multi-agent systems. Stochastic aspects have been studied in modeling agents’ behavior in consensus problems, but this approach has yet to be developed for more general settings. Second, in studying the behavior of a multi-agent system, one should consider both the perspective of the aggregate behaviour, and the perspective of the individual participants, which requires a probabilistic formulation of the associated desiderata. Finally, the number of participants changes over time, which limits the direct applicability of results from control theory and game theory.  

Within multi-agent systems, lack of interest in proving robustness of stochastic models is rooted in the fact that state-space approaches to supervision and verification of modular discrete-event systems are PSPACE-complete even in deterministic calculi, and are undecidable in some stochastic calculi. While space-efficient methods may still be possible for some special cases, radically novel methods are required to manage the state-explosion problem. In a string of recent papers, we have developed guarantees for such stochastic models of multi-agent systems, utilizing non-trivial conditions from non-linear control theory (incremental input-to-state stability), and conditions from applied probability (contractivity on average). These allow for the study of both ergodic properties of the multi-agent systems, and fairness properties from the individual point of view.