Question 2 Bob and Frank play the following sequential-move game. Bob first picks a number sg= {1,3,5,7,9) and tells it to Frank. Frank then picks a number sp = {2, 4, 6, 8, 10} in response to Bob's action. Bob has to pay (SB - SF)² so payoffs are given by UB (81, 82) = − ($1 – 82)² and UF (SB, SF) = ($₁ - $₂)². (a) (1 point) Draw the extensive form of the game. (b) (2 points) How many subgames does this game have? Define the pure strategies of each player. (c) (2 points) What is Frank's best response SF (SB) to every SÅ? (d) (4 points) Find all the pure-strategy subgame perfect equilibria of the game and give each player's payoff in these equilibria. 2 (e) (1 point) Does the game have a pure-strategy Nash equilibrium that leads to different payoffs than those you found in part (d)? If yes, show it. If not, explain why not.