Fred and Barney are playing the centipede game, which works as follows. Each player starts with a pile of money containing $2, Fred moves first; then they alternate turns. On each turn, a player says either stops or continues. If he says stop, the game ends and each player keeps the money in his own pile. If he says continue, $1 is removed from his own pile and $2 is added to the other player's pile, after which the next player takes his turn. The game must end when each player's pile contains $10 (which the players keep). Illustrate this game by drawing a tree and solve it by reasoning in reverse. Do you think people would actually play the game this way? Why or why not? How would your answer change if the game ended only when each pile contained $100?