The money-grenade game with commitment Consider the money-grenade game covered in Lecture 4. Now, suppose that Player 2's grenade is synced with a deposit machine that has the following four modes: (i) ignite the grenade in 30 seconds unless a deposit of $1000 is made to Player 2, (ii) ignite the grenade in 30 seconds if a deposit of $1000 is made to Player 2; otherwise, don't ignite, (iii) always ignite the grenade in 30 seconds, and (iv) never ignite the grenade Before Player 1 decides whether to give $1000 to Player 2 or to keep the money, Player 2 switches the machine to one of these modes. Once switched, the mode cannot be changed. a. Write down the extensive-form representation of this game (i.e., the game tree). b. Find the subgame perfect equilibrium using backward induction. c. Is there any Nash equilibrium in which Player 1 keeps the money?