Consider the following three player game. Player 1 begins the game by deciding whether to "stop" or "continue." If player 1 decides to stop, then the game ends and all three players get 100 dollars. If instead player 1 decides to continue, the game continues with player 2 making the same decision of "stop" or continue. If player 2 decides to stop, then again the game ends but with all three players receiving 50 = 100 / 2 dollars. If instead player

2 , decides to continue, then player 3 makes a final decision of whether to say stop or continue. If he decides to stop, then the game ends and each player receives 100 / 3 dollars. If player 3 decides to continue, then the game also ends and all three =players receive 200 dollars.

Part a: Write the extensive form representation of this dynamic game.

Part b: Is this a game of perfect information?

Part c: What are the backward induction strategy profiles of this game? What are the resulting payoffs for the players?

Part d: Suppose that we extended the above game to include 1000 players. In this modified game, players similarly line up in a line and sequentially decide whether to stop or continue. If the k -th player in line decides to stop, the game ends with all players getting 100/k dollars. On the other hand, if the k-th player decides to continue, then the (k+ 1) -th player makes the same decision of whether to stop or continue. The game continues until either a player says stop or we reach an outcome in which all 1000 players have decided to all continue. If all players decided "continue," then all players receive 200 dollars. What is the backward induction strategy profile of this game? Do you think this prediction is realistic?