Toward a Theory of Play: A Logical Perspective on Games and Interaction
Johan van Benthem, Eric Pacuit, Olivier Roy

Abstract:
Logic and game theory have had a few decades of contacts by now, with
the classical results of epistemic game theory as major
high-lights. In this paper, we emphasize a recent new perspective
toward “logical dynamics”, designing logical systems that focus on the
actions that change information, preference, and other driving forces
of agency. We show how this dynamic turn works out for games, drawing
on some recent advances in the literature. Our key examples are the
long-term dynamics of information exchange, as well as the
much-discussed issue of extensive game rationality. Our paper also
proposes a new broader interpretation of what is happening here. The
combination of logic and game theory provides a fine-grained
perspective on information and interaction dynamics, and we are
witnessing the birth of something new which is not just logic, nor
just game theory, but rather a Theory of Play.