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