Coalition formation over graphs is a well studied class of games whose players are vertices and feasible coalitions must be connected subgraphs. In this setting, the existence and computation of equilibria, under various notions of stability, has attracted a lot of attention. However, the natural process by which players, starting from any feasible state, strive to reach an equilibrium after a series of unilateral improving deviations, has been less studied. We investigate the convergence of dynamics towards individually stable outcomes under the following perspective: what are the most general classes of preferences and graph topologies guaranteeing convergence? 

To this aim, on the one hand, we cover a hierarchy of preferences, ranging from the most general to a subcase of additively separable preferences, including individually rational and monotone cases. On the other hand, given that convergence may fail in graphs admitting a cycle even in our most restrictive preference class, we analyse acyclic graph topologies such as trees, paths, and stars. 

Common-pool resources are resources that can be consumed or replenished by all agents. They can be associated with the memory shared by computer processes, or with the energy of which agents are consumers and producers in a smart-grid.

I will present work on the computational aspects of rational equilibria in the presence of common-pool resources. In particular, I will introduce quantitative extensions of the problem of rational synthesis, where agents have both temporal and quantitative objectives.

Additionally, I will discuss research on games where agents contribute resources to a common pool and aim to achieve objectives defined by specific resource requirements.