Randomization and Simplification in Dynamic Decision Making

Ehud Kalai and Eilon Solan

Journal of Economic Theory, to appear.

Randomization adds beneficial flexibility to the construction of optimal simple plans in dynamic environments. A decision maker, restricted to the use of simple plans, may find a stochastic plan that strictly outperforms all deterministic ones. This is true even in non interactive deterministic environments where the decision maker’s choices have no influence on his signals nor on the future evolution of the system. We describe a natural decomposition of simple plans into two components:

an action selection rule and a behavior modification rule.

In non interactive environments optimal simple plans do not require randomization in the action selection rule. Only randomization in the behavior modification rule may be necessary.