Consider the extensive-form game shown in given Figure.
a. Find two pure-strategy equilibria and show that only one of them is a sequential-equilibrium scenario (see Selten, 1975; Binmore, 1987- 88).
b. Let e be an arbitrarily small positive number. Suppose that there is a payoff-irrelevant event that has a probability e of occurring before this game is played and that, if it occurred, would be observed by players 1 and 3 but not by player 2.
Show the extensive-form game where this event is taken into account and show that this revised game has a sequential equilibrium in which, if the e-probability event does not occur, the players behave according to the equilibrium that, by your answer to part (a), was not a sequential-equilibrium scenario of the original game.
