Monotone Comparative Statics in Ordered Vector Spaces

This paper considers ordered vector spaces with arbitrary closed cones and establishes a number of characterization results with applications to monotone comparative statics (Topkis (1978), Topkis (1998), Milgrom and Shannon (1994)). By appealing to the fundamental theorem of calculus for the Henstock-Kurzweil integral, we generalize existing results on increasing differences and supermodularity for C1 or C2 functions. None of the results are based on the assumption that the order is Euclidean. As applications we consider a teamwork game and a monopoly union model.