# Computing Subgame-Perfect Equilibrium

Suppose that two players play each other for two periods. In the first period they play the first game below, and in the second period they play the second game below. There is no discounting between periods. Players observe the action their opponent took in the first period before choosing their second period actions. $$\begin{bmatrix}(2,2)&(-10,x)\\(y,0)&(0,0)\end{bmatrix}$$ $$\begin{bmatrix}(8,4)&(0,0)\\(0,0)&(4,8)\end{bmatrix}$$

(a) For x ≤ 2 and y ≤ 6, find a subgame perfect equilibrium in which player 1 receives a payoff of 10. (b) For x = 5 and y = 3 find a subgame perfect equilibrium in which player 2 receives a payoff of 10. (c) For x = y = 4, show that there is no subgame perfect equilibrium in which (U,L) is played in the first period.

I'm totally lost as how to find subgame perfect equilibria. Aren't these games simultaneous games? Why would the players consider the choices made in the first game to play the second game?