1. (DSR, Chp 6, U7) The members of a hierarchical group of three hungry lions face a piece of prey. If lion 1 does not eat the prey, the game ends. If it eats the prey, it becomes fat and slow, and lion 2 can eat it. If lion 2 does not eat lion 1, the game ends; if it eats lion 1 then it may be eaten by lion 3. Each lion prefers to eat and stay alive (payoff=4) than to stay alive but go hungry (payoff =3), but prefers to be hungry than to be eaten (payoff=2). (a) Draw the game tree, with payoffs, for this hungry lion game, and find the subgame perfect equilibrium. (b) Write out this game in normal form. Make lion 1 the row player, lion 2 the column player, and lion 3 the page/table player. (c) Find all of the Nash equilibria for the game. (d) You should have found Nash equilibria that are not subgame-perfect. For each of those equilibria, which lion is making a noncredible treat? Explain.
