Consider the extensive form game in Fig 7.41. Each of players 1, 2, and 3 can play down (d) or across (a), and player 1 can also play left (l) or right (r).
(a) Identify all sub games.
(b) Find a pure strategy sub game perfect equilibrium, b, such that (p, b) is not sequentially rational for any system of beliefs p.
(c) Find an assessment, (p, b), that is sequentially rational and satisfies Bayes' rule in every sub game.
