2 Randomization and Simplification

Randomization may add beneficial flexibility to the construction of optimal simple decision rules in dynamic environments. A decision maker, restricted to the use of simple rules, may find a stochastic rule that strictly outperforms all deterministic ones. This is true even in highly separable Markovian environments where the set of feasible choices is stationary and the decision maker’s choices have no influence on future payoff functions. In separable environments, however, the period selection of an action can still be deterministic; only the transitions in the evolution of his behavior may require randomization. 1 MEDS Dept., Kellogg Graduate School of Management and Dept. of Mathematics, College of Arts and Sciences, Northwestern University, Evanston IL 60208-2001. email: [email protected]. Kalai wishes to acknowledge financial support from the National Science foundation, grant number SES 9904931 2 MEDS Dept., Kellogg Graduate School of Management, Northwestern University, Evanston IL 60208-2001. e-mail: [email protected]. 3 The authors wish to thank Adam Kalai and Ehud Lehrer for helpful conversations.