Article

Journal of Logic, Language and Information

, Volume 19, Issue 3, pp 327-351

First online:

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

  • Emiliano LoriniAffiliated withInstitut de recherche en informatique de Toulouse, Université de Toulouse, CNRS Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.

Keywords

Coalition logic Game theory