Consider the three-player extensive-form game depicted in figure 3.21.
(a) Show that (A, A) is not the outcome of a Nash equilibrium.
(b) Consider the nonequilibrium situation where player 1 expects player 3 to play R, player 2 expects player 3 to play L, and consequently players
1 and 2 both play A. When might this be a fixed point of a learning process like those discussed in chapter 1? When might learning be expected to lead players 1 and 2 to have the same beliefs about player 3's action, as required for Nash equilibrium? (Give an informal answer.) For more on this question see Fudenberg and Kreps 1988 and Fudenberg and Levine 1990.