1. Consider the following description of a two-player extensive form game. Player one (she) moves first and selects between actions X,Y, and Z: If she chooses X the game ends and both players receive a payoff of one. If she selects Y or Z; then player two (he) sees that she did not choose X but does not see which of Y or Z she chose. Player two then chooses between L and R. If he chooses L; both players get a payoff of zero. If player one chose Y and player two chose R, then both players get a payoff of two. If payer one chose Z and player two chose R; then player one sees what has happened and chooses T or B. If he chooses T , then both players get a payoff of five. If player one instead chooses B; they both receive a payoff of negative one.

(a)Carefully draw the game tree for this game. How many subgames are there? How many information sets?

(b)List the pure strategy sets for both players.

(c)Find the pure strategy Nash equilibria (NE).

(d) Find the pure strategy subgame perfect Nash equilibria (SPNE)