New characterizations of M-convex functions and their applications to economic equilibrium models with indivisibilities. (Q1410697)

The authors study and apply the concept of M\(^\natural\)-convex functions, a variation of the concept of M-convex functions employed in convex analysis on discrete spaces. New characterizations of M\(^\natural\,\)-convexity are provided in terms of conditions originating in economic models, like Gross Substitutability or Single Improvement. These results are then applied to an existence theorem for exchange equilibria of economies with money and indivisible goods. Existence is obtained with the sole assumption of M\(^\natural\,\)-convexity (besides some more basic ones), and this is shown to be equivalent to another assumption used before to get existence but also to other ones under which existence had not yet been proved.