Pennsylvania State University ECON 402Midterm 2 - solutions 1 

Q1:
a: Here is the extensive form of the game:
1
2
2, 2
G
-1, -1
G D
2
0, 4
G
0, b
D
D
b: Here is the normal form of the game:
GG GD DG DD
G 2, 2 2, 2 -1, -1 -1, -1
D 0, 4 0, b 0, 4 0, b
Here for Player 2’s strategies, for instance GD denotes the strategy where
Player 2 plays the action G (for Go) when Player 1 plays G and Player 2 plays
the action D (For Don’t Go) when Player 2 plays D.
c: We see that Player 1’s strategies cannot dominate each other (G is a best
response to GG and D is a best response to DD). For Player 2, GD dominates
DG (2 > -1 and 5 > 4). There is no other domination. As we assume that the
players are rational, we can say that Player 2 is not going to play DG and that
is all we can say. Any strategy profile that doesn’t include DG can be played
by rational players.
d: After removing DG, we notice that Player 1’s strategies are still best responses to GG and DD respectively. Moreover, none of the remaining strategies
of Player 2 dominates each other as we have already said. Hence, our conclusion
is the same as above.
e: When we look at the best responses, we see that the set of Nash Equilibria
is {(G, GG), (G, GD), (D, DD)}.
f: As before, Player 1’s strategies are undominated. For Player 2, GG dominates DD (2 > -1 and 4 > 3). There is no other domination so all we can say
is Player 2 will not play DD if all we know is that players are rational.
g: After removing DD, no further strategy can be removed for any player.
Hence, we can only say that Player 2 will not play DD even under the common
knowledge of rationality.
h: When we look at the best responses, we see that the set of Nash Equilibria
is {(G, GG), (G, GD), (D, DG)}.