This paper studies cooperation and morality in economics, with regard to the so-called Kantian behavior. I propose a theory for interpreting the Kantian universalization principle in egalitarian terms, when agents are asymmetrically situated. As such, equivalent strategies are those that, if played jointly, yield equal payoff gains to the agents, with respect to some reference outcome. I show that the resulting equivalence relation satisfies a consistency property: agents optimizing under the constraint of universalistic morality choose indeed equivalent strategies. The outcome of agents' interaction corresponds to the egalitarian solution in the associated bargaining problem, which is Pareto-efficient under mild regularity conditions. I present two applications in a game of public good provision and in a voting model with costly turnout.