A Dynamic Logic of Agency II: Deterministic DLA, Coalition Logic, and Game Theory

摘要

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 DDLA (Deterministic Dynamic logic of Agency) which supports reasoning about actions and joint actions of agents and coalitions, and agentive and coalitional capabilities. In VVCA it is supposed that, once all agents have selected a joint action, the effect of this joint action is deterministic. In order to assess DDLA we prove that it embeds Coalition Logic. We then extend 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.