1
00:00:06,086 --> 00:00:07,576
>> Let's talk a little
bit about game theory.

2
00:00:08,406 --> 00:00:10,896
Some times in economics
people want to be able

3
00:00:10,896 --> 00:00:12,706
to describe situations

4
00:00:12,706 --> 00:00:15,096
that involve what we call
strategic interaction.

5
00:00:15,936 --> 00:00:17,806
Strategic interaction just means

6
00:00:17,806 --> 00:00:22,076
that now not only does your pay
off, your profit, your utility,

7
00:00:22,076 --> 00:00:25,856
how ever you want to think about
it depend on your own choices

8
00:00:26,286 --> 00:00:29,376
but it also depends on the
choices of other people

9
00:00:29,376 --> 00:00:32,916
in your market, in your
industry and so on and so forth.

10
00:00:33,996 --> 00:00:37,096
Typical examples of strategic
interaction usually involves

11
00:00:37,096 --> 00:00:39,486
decision among firms
regarding whether

12
00:00:39,486 --> 00:00:42,246
to cooperate or to compete.

13
00:00:42,906 --> 00:00:44,356
We're going to go
over and example

14
00:00:44,356 --> 00:00:46,396
that has a slightly
different context known

15
00:00:46,396 --> 00:00:49,696
as the prisoner's dilemma where
people are deciding whether

16
00:00:49,696 --> 00:00:52,336
or not to confess to
a particular crime.

17
00:00:52,476 --> 00:00:56,476
The set up of the prisoner's
dilemma is a tad bit contrived

18
00:00:56,576 --> 00:00:57,556
but it goes as follows.

19
00:00:58,456 --> 00:01:01,376
Imagine a situation in
which two people are brought

20
00:01:01,576 --> 00:01:03,236
in for supposedly
committing a crime.

21
00:01:04,066 --> 00:01:06,306
Now these two people are
held in separate cells

22
00:01:06,306 --> 00:01:08,506
so they can't talk to
each other and even

23
00:01:08,506 --> 00:01:11,316
if they could they couldn't
somehow contract on whether

24
00:01:11,316 --> 00:01:12,716
or not they were going
to confess to the crime.

25
00:01:14,236 --> 00:01:16,356
The people are then
brought in individually

26
00:01:16,506 --> 00:01:19,326
and asked do you confess
or do you not confess?

27
00:01:20,656 --> 00:01:23,606
We can represent the pay off's
to that sort of situation

28
00:01:24,296 --> 00:01:25,526
in a table as follows.

29
00:01:25,916 --> 00:01:31,456
You'll notice here that we
have player 1 and player 2.

30
00:01:31,456 --> 00:01:33,656
I made things nicely color coded

31
00:01:33,656 --> 00:01:37,756
such that we have player 1's
pay off's in terms of utility

32
00:01:38,796 --> 00:01:43,136
in blue to match play 1 and
player 2's pay off's in terms

33
00:01:43,136 --> 00:01:45,586
of utility in green here.

34
00:01:47,106 --> 00:01:51,386
So you'll notice that if neither
player confesses they just sit

35
00:01:51,386 --> 00:01:54,616
there and hold tight, they
each get a pay off of 10.

36
00:01:55,896 --> 00:01:59,566
If the first guy keeps quiet
and the second guy rats him

37
00:01:59,566 --> 00:02:05,216
out the second guy gets 15 while
the first player gets nothing.

38
00:02:06,546 --> 00:02:10,756
The opposite happens here
if the first player rats

39
00:02:10,756 --> 00:02:13,756
out the second one, now
the first player gets 15

40
00:02:14,156 --> 00:02:15,516
and the second player
gets nothing.

41
00:02:16,566 --> 00:02:19,556
And if they both try to rat
each other out, they both end

42
00:02:19,556 --> 00:02:24,156
up with 5 meaning they're better
off than if they just sat here

43
00:02:24,156 --> 00:02:27,066
and had the other guy
rat him out but not quite

44
00:02:27,066 --> 00:02:30,786
as well off collectively
as if they both kept quiet.

45
00:02:31,626 --> 00:02:38,236
The question then becomes given
this structure what's going

46
00:02:38,236 --> 00:02:38,606
to happen.

47
00:02:38,606 --> 00:02:40,746
In reality both players are
making the decision of whether

48
00:02:40,856 --> 00:02:44,996
or not to confess at the same
time but let's just pretend

49
00:02:44,996 --> 00:02:46,816
that they can guess or somehow
know what the other person is

50
00:02:46,816 --> 00:02:50,376
going to do and we can ask a
number of hypothetical questions

51
00:02:50,706 --> 00:02:54,346
as to what the best response
is for these players would be.

52
00:02:54,346 --> 00:02:57,206
So let's take the
first case here,

53
00:02:58,116 --> 00:03:02,256
say if player 1 confesses
what should player 2 do?

54
00:03:02,256 --> 00:03:04,996
In other words what's
player 2's best response?

55
00:03:06,366 --> 00:03:07,566
Well, we can go over here,

56
00:03:08,286 --> 00:03:11,746
we say if player 1
confesses we're somewhere

57
00:03:11,856 --> 00:03:18,286
in the bottom here and player 2
can either get zero by holding

58
00:03:18,286 --> 00:03:22,456
out and being quiet or he
can get 5 by confessing also.

59
00:03:23,506 --> 00:03:28,516
Five is strictly better than
zero so if player 1 confesses,

60
00:03:28,566 --> 00:03:36,746
player 2 also wants to confess.

61
00:03:37,086 --> 00:03:39,116
Now what about if
player 1 doesn't confess,

62
00:03:40,066 --> 00:03:44,556
well if player 1 doesn't
confess we're up here

63
00:03:44,766 --> 00:03:48,196
so player 2 again has two
options, he can get 10

64
00:03:48,196 --> 00:03:53,616
by keeping quiet or he can get
15 by ratting out his buddy.

65
00:03:54,666 --> 00:03:59,146
So 15 is better than 10 so
if player 1 doesn't confess,

66
00:04:00,776 --> 00:04:08,766
player 2 still should confess.

67
00:04:08,886 --> 00:04:13,886
Notice here that's interesting
that player 2 his best option is

68
00:04:13,886 --> 00:04:17,736
to confess regardless
of what player one does

69
00:04:18,326 --> 00:04:21,256
or alternatively put
player 2's best option is

70
00:04:21,326 --> 00:04:25,016
to confess regardless of what he
thinks player 1 is going to do.

71
00:04:26,256 --> 00:04:30,336
This type of situation is
called a dominant strategy

72
00:04:30,736 --> 00:04:33,126
in that confess is
a dominant strategy

73
00:04:33,186 --> 00:04:35,886
for player 2 meaning it's
always the best regardless

74
00:04:35,886 --> 00:04:36,826
of what the other guy does.

75
00:04:37,976 --> 00:04:40,966
Think about this the other way
around, say we make some guesses

76
00:04:40,966 --> 00:04:44,446
as to what player 2 is going
to do and then when we say

77
00:04:44,446 --> 00:04:47,406
in each case what's player 1's
best response in that situation.

78
00:04:49,136 --> 00:04:50,926
So if player 2 confesses,

79
00:04:51,526 --> 00:04:54,916
what's the best thing
for player 1 to do?

80
00:04:55,166 --> 00:04:57,726
Say if player 2 confesses
we're over here

81
00:04:57,726 --> 00:05:02,646
on the right somewhere we
say player 1 can either get 5

82
00:05:02,996 --> 00:05:07,886
by confessing or 0 for being
quiet this problem is looking

83
00:05:07,886 --> 00:05:11,126
strangely familiar, say
well 5 is better than 0

84
00:05:11,376 --> 00:05:16,966
so player 1 is going
to want to confess.

85
00:05:18,696 --> 00:05:22,236
Now if player 2 doesn't
confess what should player 1 do?

86
00:05:23,966 --> 00:05:26,916
So if player 2 doesn't
confess, we're over here

87
00:05:26,916 --> 00:05:30,736
on the left somewhere and
player 1 can either get 10

88
00:05:30,986 --> 00:05:34,006
by being quiet or 15 by
ratting out his buddy,

89
00:05:34,516 --> 00:05:44,836
well 15 is greater than 10 so
he's going to want to confess.

90
00:05:44,966 --> 00:05:46,936
Notice here that
because we confessed

91
00:05:47,076 --> 00:05:51,626
in both cases confessing
is also a dominant strategy

92
00:05:52,066 --> 00:05:53,686
for player 1.

93
00:05:54,986 --> 00:05:58,836
So here I've circled player
2's best responses in green

94
00:05:59,316 --> 00:06:02,996
and I've circled player
1's best responses in blue

95
00:06:04,126 --> 00:06:06,906
and you'll notice there's one
place here where they over lap

96
00:06:07,606 --> 00:06:11,886
to say that in this situation
where both parties confess both

97
00:06:11,886 --> 00:06:15,176
of them are responding
as best they can

98
00:06:15,786 --> 00:06:18,506
to what they think the other
person is going to be doing.

99
00:06:19,736 --> 00:06:22,536
We say that this situation
here is what's called a Nash

100
00:06:22,726 --> 00:06:27,656
equilibrium; more formally put a
Nash equilibrium is a situation

101
00:06:27,656 --> 00:06:31,446
where each player's
action is the best response

102
00:06:31,886 --> 00:06:34,506
to the other player's actions.

103
00:06:35,256 --> 00:06:38,486
In a situation where the players
are all moving simultaneously

104
00:06:38,756 --> 00:06:41,926
this basically means that
each player is reacting best

105
00:06:42,096 --> 00:06:44,276
to what they think the
other person is going to do

106
00:06:44,746 --> 00:06:46,416
and they're actually
right in their guess

107
00:06:46,416 --> 00:06:48,476
of what the other
person is going to do.

108
00:06:55,516 --> 00:07:01,996
[ Pause ]

109
00:07:02,496 --> 00:07:06,796
Notice here that the equilibrium
outcome actually...it doesn't

110
00:07:06,796 --> 00:07:09,736
look as good as it could
because here we're saying

111
00:07:09,736 --> 00:07:12,556
that any equilibrium when
people are acting according

112
00:07:12,556 --> 00:07:15,556
to their own best interest each
of them ends up with a payout

113
00:07:15,556 --> 00:07:19,396
of 5 where as if they only
cooperated they would each get a

114
00:07:19,396 --> 00:07:21,706
payout of 10.

115
00:07:21,786 --> 00:07:26,786
We can say here that there can
be a perato improvement going

116
00:07:26,786 --> 00:07:30,836
from both parties confessing
to both parties staying quiet

117
00:07:31,376 --> 00:07:33,586
in that both parties
would be made better off

118
00:07:34,406 --> 00:07:36,286
and nobody would
be made worse off.

119
00:07:37,666 --> 00:07:39,836
Unfortunately, due to
the competitive nature

120
00:07:39,836 --> 00:07:42,736
of the this game that's
not what's going to result

121
00:07:42,736 --> 00:07:46,126
because it's really hard when
there's no contracting involved

122
00:07:46,806 --> 00:07:50,716
to guarantee regardless of
what the other party says then

123
00:07:50,716 --> 00:07:52,556
when it comes down to it
they're actually going

124
00:07:52,556 --> 00:07:54,226
to cooperate given that it's

125
00:07:54,226 --> 00:07:57,286
in their interest
individually to not cooperate.

126
00:07:58,446 --> 00:08:00,206
So one question that
economists like to think

127
00:08:00,206 --> 00:08:04,056
about is then how can
cooperation be sustained

128
00:08:04,056 --> 00:08:04,976
in the real world?

129
00:08:05,606 --> 00:08:07,256
Well, one thing that's
important to remember here is

130
00:08:07,256 --> 00:08:11,536
that in the real world this
game isn't played just once,

131
00:08:12,026 --> 00:08:13,496
when you have firms interacting

132
00:08:13,496 --> 00:08:16,956
with each other people making
these decisions often times they

133
00:08:17,016 --> 00:08:19,676
have the chance to make the
decisions over and over and over

134
00:08:19,676 --> 00:08:24,586
so when you have what's called
a repeated game you might have a

135
00:08:24,586 --> 00:08:27,096
situation where people
start testing out the waters

136
00:08:27,246 --> 00:08:30,196
to say well maybe if I
cooperate the other guy's going

137
00:08:30,196 --> 00:08:32,866
to cooperate and then
we can keep this going

138
00:08:33,926 --> 00:08:39,106
because to cooperate here and
hope for the best outweighs,

139
00:08:39,106 --> 00:08:41,216
you know there's this
threat of well if you try

140
00:08:41,216 --> 00:08:44,466
to screw me one time we're
reverting back here actually

141
00:08:44,466 --> 00:08:47,666
gives in the long term an
incentive to cooperate.

142
00:08:48,836 --> 00:08:51,516
So like I said it seems a little
bit artificial to be talking

143
00:08:51,516 --> 00:08:54,956
about this context of
prisoners being interrogated

144
00:08:55,716 --> 00:09:00,706
because really we're
talking about economics.

145
00:09:01,846 --> 00:09:08,066
But it's very easy to see how
this situation could be relevant

146
00:09:08,066 --> 00:09:10,756
in an economic context by just
replacing the intuition behind

147
00:09:10,756 --> 00:09:11,276
some of the choices.

148
00:09:11,276 --> 00:09:14,006
So what I did here is
set up the identical game

149
00:09:14,226 --> 00:09:21,536
and have this model as
still player 1 and player 2

150
00:09:21,536 --> 00:09:25,526
but now they have the
choice of whether or not

151
00:09:25,686 --> 00:09:26,656
to cooperate or to compete.

152
00:09:26,656 --> 00:09:32,316
And you can see here they'd both
do better off by cooperating

153
00:09:32,316 --> 00:09:35,156
but they also all have the
private incentive to compete.

154
00:09:35,436 --> 00:09:38,406
And you can notice here

155
00:09:38,406 --> 00:09:41,486
that this situation is
actually pretty realistic

156
00:09:42,926 --> 00:09:47,816
because at least in the United
States firms are not allowed

157
00:09:47,846 --> 00:09:49,226
to contract on whether or not
they're going to cooperate,

158
00:09:49,256 --> 00:09:50,096
that's called collusion,
it's illegal.

159
00:09:50,126 --> 00:09:51,116
So they really are
simultaneously making

160
00:09:51,146 --> 00:09:52,376
independent choices as
to how much to cooperate

161
00:09:52,406 --> 00:09:52,976
with their ''competitors''.