  In several game situations, the behavior of the players may depend not only
on individual interests, but also on what each player considers as the correct
thing to do. This work presents a game theoretic model, aiming to describe game
situations in which the players' behavior is affected by ethical
considerations. Particularly, we assume that they partially follow, Kant's
`Categorical Imperative'. The model is stated for games with a continuum of
players. The basic assumption made is that the participants perceive that they
belong to virtual (imagined) groups, in which they optimize their actions as if
they were bound to follow the same strategy. A partially cooperative
equilibrium, called $r$-Kant-Nash equilibrium is then introduced. We then study
the relationship of the $r$-Kant-Nash equilibrium with the Nash, (Bentham-)
Harsanyi, Rawls difference and Roemer solutions. For the case where the set of
possible player types is finite, we prove sufficient conditions for the
existence and uniqueness of the $r$-Kant-Nash equilibrium and the equilibrium
is characterized in terms of a variational inequality. For the case of
continuous types, necessary conditions characterizing the partial Kantian
equilibria are derived using a reduction to a set of optimal control problems.
Finally, some numerical examples are given.
