Assignment:
(a) Let i be a player with perfect recall in an extensive-form game and let σi be a mixed strategy of player i. Suppose that there is a strategy vector σ−i of the other players such that ρ(x; σi, σ−i) > 0 for each leaf x in the game tree. Prove that there exists a unique behavior strategy bi equivalent to σi.
(b) Give an example of an extensive-form game in which player i has perfect recall and there is a mixed strategy σi with more than one behavior strategy equivalent to it.
Provide complete and step by step solution for the question and show calculations and use formulas.