1. The Following Game between Kyle and John begins after Kyle has lost an election between the two. If Kyle Accepts the election result, the game ends and he gets a payoff of -30, while John gets a payoff of 40. If Kyle Rejects the result, John must de- cide whether to Concede or to Fight. If John Concedes, the game ends and Kyle gets a payoff of 30, while Joe gets a payoff of -10. If John Fights, Kyle must choose whether to Escalate or Not escalate. After this choice, John must decide whether to pur- sue a Peaceful or Violent Protest. If he chooses Peace, Joe gets a payoff of 30 when Kyle chooses Not escalate but a payoff of -20 if Kyle chooses Escalate. If he chooses Violence, John gets a payoff of 10 when Kyle chooses Not escalate but a payoff of 20 if Kyle chooses Escalater. If Kyle chooses Escalate, he gets a payoff 40 if John chooses Peaceful but 10 if he chooses Violent. If Kyle chooses Not escalate, he gets a payoff -10 if John chooses Peaceful but 20 if he chooses Violent.

(i) (a) Draw the game tree of this game.

(b) Represent this as a normal form game (a matrix) and find all the pure-strategy Nash equilibria.

(c) Find all the Subgame Perfect Nash Equilibria in this game. How many are there? Why should we expect this to be the number of SPNE?