A slave has just been thrown to the lions in the Roman Colosseum. Three lions are chained down in a line, with Lion 1 closest to the slave. Each lion’s chain is short enough that he can only reach the...

A slave has just been thrown to the lions in the Roman Colosseum. Three lions are chained down in a line, with Lion 1 closest to the slave. Each lion’s chain is short enough that he can only reach the two players immediately adjacent to him. The game proceeds as follows. First, Lion 1 decides whether or not to eat the slave. If Lion 1 has eaten the slave, then Lion 2 decides whether or not to eat Lion 1 (who is then too heavy to defend himself). If Lion 1 has not eaten the slave, then Lion 2 has no choice: he cannot try to eat Lion 1, because a fight would kill both lions. Similarly, if Lion 2 has eaten Lion 1, then Lion 3 decides whether or not to eat Lion 2. Each lion’s preferences are fairly natural: best (4) is to eat and stay alive, next best (3) is to stay alive but go hungry, next (2) is to eat and be eaten, and worst (1) is to go hungry and be eaten.

(a) Draw the game tree, with payoffs, for this three-player game.

(b) What is the rollback equilibrium to this game? Make sure to describe the strategies, not just the payoffs.

(c) Is there a first-mover advantage to this game? Explain why or why not.

(d) How many complete strategies does each lion have? List them.