4. Consider the following game. There are two players and two possible simultaneous move games A and B. Player 1 first chooses which game is to be played; both player observe which game is played and choose their strategy. The payoff matrices for Game A and B are given by : L R L R Game A Game B : U (10,5) (0,0) U (k,k) (0,0) D (0,0) (5,10) (0,0) (0,0) where k > 0. (a) Write down the extensive form of this game. (b) Assume k = 2. Solve for all subgame perfect Nash equilibria of this game. (c) Can you find a value of k such that there exists a SPNE in which player 1 chooses game B? Can you find a value of k such that all SPNE involve player 1 choosing game B