Model checking multi-agent systems, in which agents are distributed and thus may have different observations of the world, against strategic behaviours is known to be a complex problem in a number of settings. There are traditionally two ways of ameliorating this complexity: imposing a hierarchy on the observations of the agents, or restricting agent actions so that they are observable by all agents. We study systems of the latter kind, since they are more suitable for modelling rational agents. In particular, we define multiagent systems in which all actions are public and study the model checking problem of such systems against Strategy Logic with equality, a very rich strategic logic that can express relevant concepts such as Nash equilibria, Pareto optimality, and due to the novel addition of equality, also evolutionary stable strategies. The main result is that the corresponding model checking problem is decidable.

Keywords: Strategy Logic, Multi-agent systems, Imperfect Information, Verification, Formal Methods