Recent policy initiatives offer cash payments to children (and often their families) to induce better health and educational choices. These policies implicitly assume that children are especially impatient (i.e., have high discount rates); however, little is known about the nature of children's patience, how it varies across children, and whether children can even make rational intertemporal ch...

For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for n × n win-lose-draw games (i.e. (−1, 0, 1) matrix games) nonzero probabilities smaller than n are never needed. We also construct an explicit n × n win-lose game such that the unique optimal strategy uses a nonzero probability as small as n. This is done by constructing an explicit (−1, ...