social networks 101 p rof. j ason h artline and p rof. n icole i mmorlica
TRANSCRIPT
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Social Networks 101PROF. JASON HARTLINE AND PROF. NICOLE
IMMORLICA
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Announcement
Lecture is in L211 this Friday (4/17),not Pancoe!
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Guessing game
Experiment:
There are three balls in this urn, either
or
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Guessing game
Experiment:
This is called a
blue urn.
This is called a
yellow urn.
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Guessing game
Experiment: When I call your name,
1. You (and only you) will see a random ball. 2. You must then guess if the urn is a blue urn or a yellow urn, and tell the class your guess.
If you guess correctly, you will earn one point.
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What should the 1st student do?
?
??
Guess that urn is same color as ball.
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What should the 2nd student do?
?
??
1st guess was blue.
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What should the 2nd student do?
?
??
1st guess was blue.
Guess that urn is same color as ball.
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What should the 3rd student do?
?
??
1st and 2nd guesses
were blue.
Guess that urn is blue no matter what she sees!
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What should the nth student do?
?
??
First (n-1) guesses
were blue.
First 2 students told
the truth.
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If the first two guesses are blue,everyone should guess blue.
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Lecture Eight:
Information cascades
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Staring up at the sky.
Choosing a restaurant in a strange town.
Self-reinforcing success of best-selling books.
Voting for popular candidates.
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Information cascades
When:1. People make decisions sequentially,2. and observe actions of earlier people.
Information cascade: People abandon own info. in favor of inferences based on others’ actions.
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Imitation Cascade
Rational
(not simply peer pressure)
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Observations
1. Cascades are easy to start.
(every student makes same guess so long as first two students make same guess)
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Observations
2. Cascades can lead to bad outcomes.
(given blue urn, chance of seeing red ball is 1/3, so first two students guess red with prob. (1/3)2 = 1/9)
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Observations
3. Cascades are fragile.
(if a few students show the color of the ball they picked to the entire class, the cascade can be reversed)
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Conditional probability
How likely is it that the urn is yellowgiven what you’ve seen and heard?
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Time for
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Strategy for urns
A player should guess yellow if,
Pr [ yellow urn | what she saw and heard ] > ½
and blue otherwise.
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Analysis
From setup of experiment,
Pr [ ] = Pr [ ] = 1/2
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Analysis
From composition of urns,
Pr [ | ] = Pr [ | ] = 2/3
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Analysis
Suppose first student draws :
Pr [ | ] =Pr [ | ] x Pr [ ]
Pr [ ]
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Analysis
Suppose first student draws :
Pr [ | ] = x Pr [ ]
Pr [ ]
Pr [ ] =
Pr [ | ](2/3) x (1/2)
Pr [ | ] x Pr [ ]Pr [ | ] x Pr [ ]+ (2/3) x (1/2) (1/3) x (1/2) = (1/2)
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Analysis
Suppose first student draws :
then he should guess yellow.
Pr [ | ] = (2/3) > (1/2)
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Analysis
Suppose second student draws too:
Pr [ | , ]
1st student’s guess
2nd student’s draw
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Analysis
Suppose second student draws too:
by a similar analysis, so she also guesses yellow.
Pr [ | , ] > (1/2)
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Analysis
Suppose third student draws :
Pr [ | , , ]
1st student’s guess
2nd student’s guess
3rd student’s draw
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Analysis
Suppose third student draws :
Pr [ | , , ] =
Pr [ , , | ] x Pr [ ]
Pr [ , , ]
(1/3) x (2/3) x (2/3) (1/2)
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Analysis
Pr [ , , | ] x Pr [ ]
Pr [ , , ] =
Pr [ , , | ] x Pr [ ] +
(1/3) x (2/3) x (2/3) (1/2)
(2/3) x (1/3) x (1/3) (1/2)
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Analysis
Suppose third student draws :
Pr [ | , , ] =(1/3) x (2/3) x (2/3) x (1/2)
(1/3) x (2/3) x (2/3) x (1/2) + (2/3) x (1/3) x (1/3) x (1/2)
= (2/3) > (1/2)
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Analysis
The best strategy for the third student is to guess yellow no
matter what he draws.
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Other sequences# yellow guesses - # blue guesses
0
-1
-2
1
2
Blue cascade starts.
Yellow cascade starts.
1 2 3 4 5 6 7 student
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Announcement
Lecture is in L211 this Friday (4/17),not Pancoe!
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Next time
TBA