Sophisticated Strategic Choice

Abstract

We consider two-stage strategic choice problems in which a decision maker first chooses a strategy and subsequently an alternative from a nonempty subset of feasible alternatives that may depend on the strategy chosen in the first period. The preferences over alternatives that the decision maker starts out with may change after a strategy is chosen and the new preferences may depend on the chosen strategy. We consider sophisticated trajectories and provide conditions under which such trajectories exist. Then we consider problems with a finite number of strategies and alternatives. We define the sophisticated choice function and provide characterizations for its rationalizability.