(Solved): Question 6. Two players (Player 1 and 2) each bid a real number between 0 to 10 (both included). If ...
Question 6. Two players (Player 1 and 2) each bid a real number between 0 to 10 (both included). If the sum of their bids is less than or equal to 10 , each player gets a payoff equal to her own bid. If the sum of their bids is greater than 10 , they get a payoff of 0 . Therefore, the payoff for Player 1 is:
u_(1)(s_(1),s_(2))={(s_(1), if s_(1)+s_(2)<=10),(0, if s_(1)+s_(2)>10):}The payoff for Player 2 is:
u_(2)(s_(1),s_(2))={(s_(2), if s_(1)+s_(2)<=10),(0, if s_(1)+s_(2)>10):}Suppose now that Player 1 and 2 bid simultaneously. Using the no profitable deviation argument, can you show that player 1 bids 2 and player 2 bids 8 is a Nash equilibrium? Find at least 3 other Nash equilibria of this game when Player 1 and 2 bid simultaneously. Now consider the case where player 1 moves first and player 2 moves next. Find a Subgame Perfect Nash Equilibrium (SPNE) of this game. (Hint: in the SPNE you find, you should specify explicitly
s_(1)and
s_(2), i.e., how much would Player 1 and Player 2 bid, respectively).
