Game equivalence and expressive power of game description languages: a bisimulation approach

Bisimulations are a key notion to study the expressive power of a modal language. This paper studies the expressivity of Game Description Language (GDL) and its epistemic extension Epistemic GDL (EGDL) through a bisimulation approach. We first define a notion of bisimulation for GDL and prove that it coincides with the indistinguishability of GDL formulas. Based on it, we establish a characterization of the definability of GDL in terms of $k$-bisimulations. Then we design novel notions of bisimulation for EGDL and obtain characterizations of the expressive power of EGDL in terms of them. These characterizations provide a powerful tool to identify the expressive power of game description languages. Finally, we demonstrate with real games that bisimulation can be generalized to capture a wide range of game equivalence.