Supplementary Appendix of “ Time Lotteries ”

, where u : X ! R+ is continuous and strictly increasing, and D : N ! (0, 1] is a strictly decreasing discount function. A function D is discretely convex if it is convex for all points in its domain, that is, ↵D (t1) + (1 ↵)D (t2) D (↵t1 + (1 ↵) t2) for all t1, t2 2 N and ↵ 2 (0, 1) with ↵t1 + (1 ↵) t2 2 N. A function D is discretely concave if D is discretely convex. The following proposition establishes the relationship between attitudes towards time lotteries and the convexity of the discount function: Proposition A.1. Suppose T = N. Under EDU, preferences are RSTL if and only if D is discretely convex. Moreover, they cannot be RATL. Proof. First, we show that preferences are RSTL (RATL) if and only if D is discretely convex (concave). The value of (x,t) is