文档介绍：The Electronic Mail Game: Strategic Behavior Under "Almost Common Knowledge"
Ariel Rubinstein
The American Economic Review(Jun.,1989)
Presented by Cui Zhipeng
1
The Coordinated Attack Story
Army 1
Army 2
Enemy
Attack at dawn
I see
I see you see
I see you see I see
Attack at dawn or not
Attack at dawn or not
2
Contributions of the paper
The main message of this paper is that players' strategic behavior under "almost
common knowledge" may be very different from that under common knowledge.
“Almost Common Knowledge“
VS
“Common Knowledge”
3
Definition of these two kind knowledge
Common knowledge:
it is common knowledge between two players 1and 2 that The played game is G,
if both know that the game is G,
1 knows that 2 knows that the game is G.
And 2 knows that 1 knows that the game is G,
1 knows that 2 knows that 1 knows that the game is G.
And 2 knows that 1 knows that 2 knows that the game is G
and so on and so on.
“Almost common knowledge”: not so on and so on, the “knows” are finite.
4
Introduce an example
Two players, 1 and 2, are involved in a coordination problem. Each has to choose between two actions A and B. There are two possible states of nature, a and b. Each of
the states is associated with a payoff matrix as follows:
The Game Ga
2
1
A
A
B
B
M
M
0
0
0
0
-L
-L
State a, probability 1-p
The Game Gb
2
A
A
B
B
0
0
M
M
0
0
-L
State b, probability p
1
-L
L>M>0, p<1/2
5
Both 1 and 2 knows about which state are they in, state a or state b. And the “knows” are so on and so on.
So,
if they are in state a, the players’ best strategic behaviors are to coordinate, both choose A.
if they are in state b, the players’ best strategic behaviors are to