Question: A British game show involves a final prize. The two contestants may each choose either to Split the prize, or Claim the prize. If they Split the prize, they each get 1 2 ; if they each Claim the prize, they each get 0. If one player Splits, and the other player Claims, the player who Claims the prize gets 1 and the other player gets 0. The game matrix is
(a) Find the Nash bargaining solution without threats.
(b) Apparently, each player has a credible threat to always Claim the prize. Find the optimal threat strategies and the Nash solution as well as the combination of pure strategies that the players should agree to in the threat game.
(c) If the game will only be played one time and one player announces that he will definitely Claim the prize and then split the winnings after the show is over, what must the other player do?