Language is a powerful coordination device. We generalize the cheap-talk approach to pre-play communication by way of introducing a meaning correspondence between messages and actions, and by postulating two axioms met by natural languages. Players have a lexicographic preference, second to...

Perfect information games have a particularly simple structure of equilibria in the associated normal form. For generic such games each of the finitely many connected components of Nash equilibria is contractible. For every perfect information game there is a unique connected and contractible...