Simon Fraser University
ECON 302
Spring 2016
S. Lu
Problems on Subgame Perfection
To Do before the Midterm
1. Consider the following 2-player game. Player 1 first picks In or Out. If he picks In, the
players play the following simultaneous-move game:
Left
Right
Top
1,1
0,0
Bottom
0,0
1,1
If player 1 picks Out, the players instead play the following simultaneous-move game:
NDP
Conservative
High
1,0
0,1
Low
0,1
1,0
a)
b)
c)
d)
Draw the extensive form of this game.
How many subgames are there, and which are they?
Find all subgame-perfect equilibria.
Give an example of a Nash equilibrium that is not a subgame-perfect equilibrium, if any,
and defend your answer.
2. Consider a game G consisting of the following 3x3 simultaneous-move game played twice;
both players observe the outcome of stage 1 before playing stage 2.
Left
Centre
Right
Top
2,2
1,0
-5,-10
Middle
0,1
0,0
-5,-10
Bottom
-10,-5
-10,-5
-10,-10
Call the first playing of the above 3x3 game “stage 1” and the second playing “stage 2.”
Assume that before playing stage 2, players see everyone’s action from stage 1. Also assume
that the total payoffs in game G are the sum of the payoffs from the two stages.
a) Draw a partial extensive form of G: your game tree should fully show stage 1, and should
show stage 2 after (Middle, Left); it need not show stage 2 after other stage 1 outcomes.
b) Find the SPE(s) of G.
c) Write down a pure-strategy NE of G with (Top, Centre) as the stage 1 outcome. Is your
answer also an SPE? Why or why not?
[Hint: Remember that in a NE, what occurs in stage 2 if the desired stage 1 outcome is
not achieved need not be credible.]