Online Appendix for Behavioral Equilibrium in Economies with Adverse Selection A. A Class of Games with Monotone Selection

This section presents a setup that arises frequently in adverse selection settings and provides conditions on the primitives such that the properties that de…ne a game with monotone selection are satis…ed. The following de…nitions and results (in addition to those in the print appendix) are used: A correspondence : T ! X is increasing in the strong set order if when t > t0, then for each x 2 (t) and y 2 (t0), sup(x; y) 2 (t) and inf(x; y) 2 (t0). A function f : X ! R is supermodular if for all x; y 2 X , f(inf(x; y)) + f(sup(x; y)) f(x) + f(y). A function g : X T ! R has increasing di¤erences in its arguments (x; t) if g(x; t) g(x; t0) is nondecreasing in x for all t t0. A function with increasing di¤erences in (x; t) is also single-crossing in (x; t), but the reverse need not hold.