Incentive compatibility and differentiability: New results and classic applications

We provide several generalizations of Mailath?s (1987) [9] result that in games of asymmetric information with a continuum of types incentive compatibility plus separation implies differentiability of the informed agent?s strategy. The new results extend the theory to classic models in finance such as Leland and Pyle (1977) [8], Glosten (1989) [4], and DeMarzo and Duffie (1999) [3], that were not previously covered.