  Traditional game theory assumes that the players in the game are aware of the
rules of the game. However, in practice, often the players are unaware or have
only partial knowledge about the game they are playing. They may also have
knowledge that other players have only partial knowledge of the game they are
playing, which they can try to exploit. We present a novel mathematical
formulation of such games. We make use of Kripke semantics, which are a way to
keep track of what different players know and do not know about the world. We
propose a notion of equilibrium for such games, and show that equilibrium
always exists.
