A Dynamic Logic of Agency II: Deterministic $${\mathcal{DLA}}$$ , Coalition Logic, and Game Theory

Abstract

We continue the work initiated in Herzig and Lorini (J Logic Lang Inform, in press) whose aim is to provide a minimalistic logical framework combining the expressiveness of dynamic logic in which actions are first-class citizens in the object language, with the expressiveness of logics of agency such as STIT and logics of group capabilities such as CL and ATL. We present a logic called $${\mathcal{DDLA}}$$ (Deterministic Dynamic logic of Agency) which supports reasoning about actions and joint actions of agents and coalitions, and agentive and coalitional capabilities. In $${\mathcal{DDLA}}$$ it is supposed that, once all agents have selected a joint action, the effect of this joint action is deterministic. In order to assess $${\mathcal{DDLA}}$$ we prove that it embeds Coalition Logic. We then extend $${\mathcal{DDLA}}$$ with modal operators for agents' preferences, and show that the resulting logic is sufficiently expressive to capture the game-theoretic concepts of best response and Nash equilibrium.