Strategies for games with state

AbstractAn application of the Chu-constructionThe construction of a symmetric monoidal closed (smc) category from tree-based games proceeds in an unusual way: first the objects are defined and easily seen to satisfy an condition typical of smc categories. Only then strategies are introduced as morphisms, and the motivation for this specific choice is based on the intuition about interaction.We present a generalization of games that takes the state of Opponent and Player into account. This allows us to use categorical criteria for the choice of useful morphisms, which turn out to be quite close to ones classical ones. The basis for this analysis is the generalized Chu-construction