This paper assesses the theory, first voiced by Schelling and Kant, according to which an infinite historical process will lead to cosmopolitan institutions.The assessment will mainly be done on the basis of theories about infinitely repeated games. The first part of the paper reconstructs “infinitesimal” historical cosmopolitanism as proposed by Schelling and Kant. The second part confronts this position with the results of the theory of infinitely repeated games among groups. The third part offers reflections on additional conditions and contingencies (...) of the theory and the forth part draws the conclusion: while we can reasonably assume global cooperation to increase and stabilize over time under sustainable conditions, we cannot predict the institutional design of that cooperation. (shrink)