1
\
2L
m
R
T
(1
,
1)
(0
,
2)
(2
,
1)
M
(2
,
2)
(1
,
1)
(0
,
0)
B
(1
,
0)
(0
,
0)
(
−
1
,
1)
Here, Players 1 has strategies, T, M, B and Player 2 has strategies L, m, R. (They
pick their strategies simultaneously.) The payo
f
s for players 1 and 2 are indicated by
the numbers in parentheses, the
f
rst one for player 1 and the second one for player 2.
For instance, if Player 1 plays T and Player 2 plays R, then Player 1 gets a payo
f
of 2
and Player 2 gets 1. Let’s assume that each player knows that these are the strategies
and the payo
f
s, each player knows that each player knows this, each player knows that
each player knows that each player knows this,.
.. ad in
f
nitum.
Now, player 1 looks at his payo
f
s, and realizes that, no matter what the other player
plays, it is better for him to play M rather than B. That is, if 2 plays L, M gives 2 and
B gives 1; if 2 plays m, M gives 1, B gives 0; and if 2 plays R, M gives 0, B gives -1.
Therefore, he realizes that he should not play B.
1