algorithms, games and the internet christos h. papadimitriou uc berkeley christos
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Algorithms, Gamesand the Internet
Christos H. Papadimitriou
UC Berkeley
www.cs.berkeley.edu/~christos
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SODA: January 8, 2001 2
• “new” vs. “old theory”• Game Theory• pricing multicast content • the price of anarchy• the economics of clustering• the economics of privacy
Outline
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SODA: January 8, 2001 3
• Goal of CS Theory (1950-2000): Develop a mathematical understanding of the
capabilities and limitations of the von Neumann computer and its software –the dominant and most novel computational artifacts of that time
(Mathematical tools: combinatorics, logic)
• What should Theory’s goals be today?
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SODA: January 8, 2001 4
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SODA: January 8, 2001 5
The Internet
• huge, growing, open, anarchic
• built, operated and used by a multitude of diverse economic interests
• as information repository: huge, available, unstructured
• theoretical understanding urgently needed
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SODA: January 8, 2001 6
• new math for the new Theory?
cf: George Boole The Laws of Thought, 1854Part I: propositional logic, Part II: probability
cf: John von Neumann The Report on EDVAC, 1945Theory of Games and Economic Behavior, 1944
(cf: Alan Turing On Computable Numbers, 1936Studies in Quantum Mechanics, 1932-35)
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SODA: January 8, 2001 7
Game Theory
Studies the behavior of rational agents in competitive and collaborative situations
Osborne and Rubinstein, A Course in GT
Kreps, A Course in Microeconomic Theory
Hart and Aumann, The Handbook of GT, volumes I and II(III, 2001 to appear)
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SODA: January 8, 2001 8
Games, games…
randominformationset
strategies
strategies3,-2
payoffs
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SODA: January 8, 2001 9
1,-1 -1,1
-1,1 1,-1
0,0 0,1
1,0 -1,-1
3,3 0,4
4,0 1,1
matching pennies prisoner’s dilemma
chicken
auction
1 … n
1
.
.
nu – x, 0
0, v – y
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SODA: January 8, 2001 10
concepts of rationality
• undominated strategy
• Nash equilibrium
• randomized Nash equilibrium ( P?)
• perfect equilibrium
• subgame perfect equilibrium
• focal point
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SODA: January 8, 2001 11
Some current areas of algorithmic interest
• repeated games (played by automata) and the emergence of cooperation
• evolutionary game theory• mechanism design: given an “economic situation,” a concept of
rational behavior, and a set of desiderata, design a game that achieves them
(e.g, Vickrey auction)
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SODA: January 8, 2001 12
e.g., pricing multicasts [Feigenbaum, P., Shenker, STOC2000]
30
2170
52
21 40
32
costs
{23, 17, 14, 9}
{14, 8}{9, 5, 5, 3}
{17, 10}
{11, 10, 9, 9}
{}
utilities of agents in the node(u = the intrinsic value of the informationagent i, known only to agent i)
i
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SODA: January 8, 2001 13
We wish to design a protocol that will result in the computation of:
• x (= 0 or 1, will i get it?)
• v (how much will i pay? (0 if x = 0) )
protocol must obey a set of desiderata:
i
i
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SODA: January 8, 2001 14
• 0 v u,
• lim x = 1
• strategy proofness: (w = u x v ) w (u …u …u ) w (u … u'…u )
• welfare maximization
w = max
marginal cost mechanism
u ii
i i
i i
defi i
i 1 i n 1 i n
i
• budget balance
v = c ( T [x])
Shapley mechanism
i
i
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SODA: January 8, 2001 15
our contribution:In the context of the Internet, there is another desideratum:
Tractability: the protocol should require few (constant? logarithmic?) messages per link. This new requirement changes drastically the space of available solutions.
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SODA: January 8, 2001 16
• 0 v u
• lim x = 1
• strategy proofness: (w = u x v ) w (u …u …u ) w (u … u'…u )
• welfare maximization
w = max
marginal cost mechanism
u ii
i i
i i
defi i
i 1 i n 1 i n
i
• budget balance
v = c ( T [x])
Shapley mechanism
i
i
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SODA: January 8, 2001 17
Bounding Nash equilibria: the price of anarchy
cost of worst Nash equilibrium“socially optimum” cost
s t 3/2 [Koutsoupias and P, 1998]
generalmulticommoditynetwork
2 [Roughgarden and Tardos, 2000]
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SODA: January 8, 2001 18
Some interesting directions:
• What is the price of the Internet architecture?
• Of which game is TCP/IP a Nash equilibrium? [Karp, Koutsoupias, P., Shenker, FOCS 2000]
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SODA: January 8, 2001 19
The economics of clustering
• The practice of clustering: Confusion, too many criteria and heuristics, no guidelines
• “It’s the economy, stupid!” [Kleinberg, P., Raghavan STOC 98, JDKD 99]
• The theory of clustering: ditto!
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SODA: January 8, 2001 20
price
quantity
q = a – b p
Example: market segmentation
Segment monopolistic market to maximize revenue
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21SODA: January 8, 2001
or, in the a – b plane:
a
b
?Theorem: Optimumclustering is by linesthough the origin(hence: O(n ) DP)
2
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SODA: January 8, 2001 22
on privacy
• arguably the most crucial and far-reaching current challenge and mission of Computer Science
• least understood (e.g., is it rational?)
• www.sims.berkeley.edu/~hal, ~/pam,
[Stanford Law Review, June 2000]
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SODA: January 8, 2001 23
• also an economic problem• surrendering private information is either good or
bad for you• personal information is intellectual property
controlled by others, often bearing negative royalty• selling mailing lists vs. selling aggregate
information: false dilemma• Proposal: Take into account the individual’s utility
when using personal data for decision-making
some thoughts on privacy
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SODA: January 8, 2001 24
e.g., marketing survey [with Kleinberg and Raghavan]
customers
possibleproducts
“likes”• company’s utility is proportional to the majority• customer’s utility is 1 if in the majority
• how should all participants be compensated?