1. Tom and Susana are playing what is known as the 'Centipede' game. Tom starts the game (white node) and can decide to stop the game or to continue. Choosing continue means passing the game over to Susana (Black decision nodes). Susana can either decide to stop or continue, etc. Each time a player chooses continue, the total payoff of the players is doubled. The initial total payoff is 5. When a player decides to 'stop', this player obtains 80% of the total current payoff, leaving 20% for the opponent. If the game reaches n rounds, the last player to decide must either choose stop dividing the current total gains 80-20 in her favor or continue and, hence doubling the total payoff but this will be divided 80-20 in favor of the opponent. The figure below illustrates a 6 round centipede game. Tom's pay-off is written in white, while Susana's is written in black. Continue Continue Continue Continue Continue Continue 256 64 Stop Stop Stop Stop Stop Stop 16 8 64 32 8 32 16 128 1.1 Solve the 6-step game by backward induction 1.2 Show that the outcome is inefficient. 1.3 How would the outcome of the game be affected if the game was extended to 100 steps, with the payoffs increasing the same manner as described above