Optimal functors in dual categories of games

Dual categories of so called non-cooperative non-strategiс games/cogames are constructed. In contrast to classical non-cooperative games, in these categories the active players differ from the interested ones, so that games and cogames associate them in two different ways. The Nash-equilibrium concept is modified for each of these categories, and it is proved that for both of them this generalized equilibrium has a fundamental categorial property – functorness. Based on that fact, a general axiomatic definition of optimal functor is given. Several optimal equilibrium-like functors are constructed, including the strongest and the weakest ones.