Nondeterministic Strategies and their Refinement in Strategy Logic

Nondeterministic strategies are strategies (or protocols, or plans) that, given a history in a game, assign a set of possible actions, all of which are winning. An important problem is that of refining such strategies. For instance, given a nondeterministic strategy that allows only safe executions, refine it to, additionally, eventually reach a desired state of affairs. We show that strategic problems involving strategy refinement can be solved elegantly in the framework of Strategy Logic (SL), a very expressive logic to reason about strategic abilities. Specifically, we introduce an extension of SL with nondeterministic strategies and an operator expressing strategy refinement. We show that model checking this logic can be done at no additional computational cost with respect to standard SL, and can be used to solve a variety of problems such as synthesis of maximally permissive strategies or refinement of Nash equilibria.