5 Simultaneous Games with 2 Players and 2 Actions
David Ronayne
22 November 2012
Ok guys, once you have digested the material on simultaneous move games, try to solve each of
the following questions for each of the games below. Once done check your answers, but please
try first before you look at the answers. One general question before you start: Will these games
have at least one NE? and why? (think Nash Existence Theorem!) For each question below,
answer:
(i) Find all the pure NE using the underlining technique
(ii) Find all the nondegenerate mixed NE (meaning NE where not all the players play one of
their strategies with probability 1)
Game 1
Player 2
Player 1
U
D
L
2,2
1,1
U
D
L
1,1
2,-1
R
0,1
1,3
Game 2
Player 2
Player 1
R
-1,2
0,0
Game 3
Player 2
Player 1
U
D
L
5,0
0,5
R
0,3
3,0
1
Game 4 - A little tricky
Player 2
Player 1
U
D
L
1,0
1,-1
R
1,0
2,2
Game 5 - Hard
Player 2
Player 1
U
D
L
2,0
1,-1
R
0,0
1,2
2