From rules to runs: A dynamic epistemic take on imperfect information games
This work addresses a foundational issue in game theory for researchers, clarifying interpretations to avoid paradoxes, but it is incremental as it builds on existing epistemic logic approaches.
The paper tackles the confusion in game theory between interpreting extensive form games as rules versus runs by proposing a dynamic epistemic framework that computes runs from rules and player assumptions, and provides a complete axiomatization for a modal logic describing knowledge changes during plays.
In the literature of game theory, the information sets of extensive form games have different interpretations, which may lead to confusions and paradoxical cases. We argue that the problem lies in the mix-up of two interpretations of the extensive form game structures: game rules or game runs which do not always coincide. In this paper, we try to separate and connect these two views by proposing a dynamic epistemic framework in which we can compute the runs step by step from the game rules plus the given assumptions of the players. We propose a modal logic to describe players' knowledge and its change during the plays, and provide a complete axiomatization. We also show that, under certain conditions, the mix-up of the rules and the runs is not harmful due to the structural similarity of the two.