The use of games to model phenomena in logic and theoretical computer science has a long history, and in the setting of modern game semantics may be summarized by the idea that propositions are not only types, but also games (and similarly, proofs are not only terms, but also strategies). This gives rise to categories of games, but from the perspective of traditional game theory a la Von Neumann and Nash the games which appear as objects of these categories are of a rather restricted nature. For example, they are necessarily two-player games. By contrast, the games studied in traditional game theory are much richer in nature, and so far no clear categorical description of traditional game theory has been given.
In this talk I will describe how traditional games may be organized and described using the language of category theory. I will also explain how many phenomena in game theory can be expressed in terms of dependent sums and products, and that the natural categorical for game theory is that of locally cartesian closed categories.