Assignment:
Q1. Prove that if a player in an extensive-form game has only one information set, then his set of mixed strategies equals his set of behavior strategies.
Q2. Does there exist a two-player zero-sum extensive-form game that has a value in mixed strategies and a value in behavior strategies, but these two values are not equal to each other? Either prove that such a game exists or provide a counterexample.
Provide complete and step by step solution for the question and show calculations and use formulas.