# Consider a sequential game which is known as the Centipede Game. In this game each of two players..

Consider a sequential game which is known as the Centipede Game. In this game, each of two players chooses between “Left” and “Right” each time he or she gets a turn. The game does not, however, automatically proceed to the next stage unless players choose to go “Right” rather than “Left”. A: Player 1 begins — and if he plays “Left”, the game ends with payoff of (1,0) (where here, and throughout this exercise, the first payoff refers to player 1 and the second to player 2). If however, he plays “Right”, the game continues and it’s player 2’s turn. If player 2 then plays “Left”, the game once again ends, this time with payoffs (0,2), but if she plays “Right”, the game continues and player 1 gets another turn. Once again, the game ends if player 1 decides to play “Left”— this time with payoffs of (3,1), but if he plays “Right” the game continues and it’s once again player 2’s turn. Now the game ends regardless of whether player 2 plays “Left” or “Right”, but payoffs are (2,4) if she plays “Left” and (3,3) if she plays “Right”. (a) Draw out the game tree for this game. What is the sub game perfect Nash Equilibrium of this game. (b) Write down the 4 by 4 pay off matrix for this game. What are the pure strategy Nash Equilibria in this game? Is the sub game perfect Nash Equilibrium you derived in (a) among these? (c) Why are the other Nash Equilibria in the game not sub game perfect? (d) Suppose you changed the (2,4) payoff pair to (2,3). Do we now have more than 1 sub ga