Two players engage in the following interaction regarding the battle of the sexes. Player 1 rst decides whether she wants to \"play" {Y} or not (N :1 If player 1 chooses N, then the game is oven and players receive payoffs (2,3). If player 1 chooses Y, then player 2 {observes player 1's choice and} decides whether he wants to \"play" (3;) or not (in). If player 2 chooses n, then the game is over, and players receive payoffs (3,2). If player 2 chooses y, then the players playr the following version of the battle of the sexes game in which they choose actions simultaneously. a h A 4,1 03,0 B 0,0 1,4 (8.} Draw the extensiveform of the game. {b} How many subgames does this game have {including the game itself)? Draw each subgame as a separate tree. (c) Find all purestrategy sub-game perfect equilibria of the game. {d} Does the game have any Nash equilibrium in which both players decide to \"play\" (i.e.J player 1 chooses Y and player 2 chooses y}