Centipedes: Imagine a two-player game that proceeds as follows. A pot of money is created with $6 in it initially. Player 1 moves first, then player 2, then player 1 again, and finally player 2 again. At each player's turn to move,
a. Model this as an extensive-form game tree. Is it a game of perfect or imperfect information?
b. How many terminal nodes does the game have? How many information sets?
c. How many pure strategies does each player have?
d. Find the Nash equilibria of this game. How many outcomes can be supported in equilibrium?
e. Now imagine that at the last stage at which player 2 moves, if he chooses to share then the pot is equally split among the players. Does your answer to part (d) change?