When are Two Games the Same? Johan van Benthem Abstract: This paper explores the interface of elementary logic and game theory, pointing out several commonalities. We search for a proper structural invariance between extensive games, using notions of bisimulation and modal languages. In this context, we also consider natural operations creating new games. The main analysis is for games with perfect information, but we sketch extensions where both knowledge and ignorance are present. The contents of this paper has been superseded by Johan van Benthem's ILLC reports of January 2003, as well as some drafts under 'current publications' on his homepage http:/staff.science.uva.nl/~johan/ Keyword(s): logic games, game equivalence, forcing bisimulation, strategy, game operations, epistemic logic