Stit Logics, Games, Knowledge, and Freedom

This paper has two main goals: highlighting the connections between Stit logics and game theory and comparing Stit logics with Matrix Game Logic, a Dynamic Logic introduced by van Benthem order to model some interesting epistemic notions from game theory. Achieving the first goal will prove the flexibility of Stit logics and their applicability in the logical foundations of game theory, and will lay the groundwork for accomplishing the second. A comparison between Stit logics and Matrix Game Logic is already offered in a recent work by van Benthem and Pacuit. Here, we push the comparison further by embedding Matrix Game Logic into a fragment of group Stit logic, and using the embedding to derive some properties of Matrix Game Logic—in particular, undecidability and the lack of finite axiomatizability. In addition, the embedding sheds light on some open issues about the so-called “freedom operator” of Matrix Game Logic.