Q1 In centipede there are two players. Player 1 moves first, player 2 moves second. After at most two moves, the game ends. The game begins with $1 sitting on a table. Player 1 can either take the $1 or wait. If player 1 takes the $1 the game is over, and player 1 gets to keep the $1. If player 1 waits the $1 quadruples to $4. Now it is player 2's turn. Player 2 can either take the entire $4 or split the $4 evenly with player 1.
a. draw the extensive form for the game of centipede
b. Illustrate what is the equilibrium to this game? Can player 2's strategy of splitting the money ever is part of an equilibrium outcome to the game?
c. Now Assume that centipede has three moves. Player 2 cannot wait, split the money or take the $4. If player 2 waits then the money on the table quadruples again and player 1 can either take it all or split it. Draw the extensive form for the new game and solve for the equilibrium outcome.