However all of that would be useless if at the same time we were not supported by a strong mathematical theory about games. During the first lecture I'll first motivate the use of games as models of interactive computation. I'll explain then the mathematical structure which has been associated to games. I'll introduce to these ideas and focus then on the mathematical notions of lattice, least and greatest fixed points, the goal being that of defining what is a mu-lattice. I'll explain why these mathematical results are of interest from the point of view of interactive computation.
References Here is a bunch of related works.
If you're interested in one of them, you'd like to attend the mini-course. A. Blass, Degrees of indeterminacy of games , 1972. A. Blass, A game semantics for linear logic , 1992. J.H. Conway, On numbers and games , 1976. H. Hu and A. Joyal, Coherence completions of categories , 1996.