algorithms, games and the internet christos h. papadimitriou uc berkeley christos

Algorithms, Gamesand the Internet

Christos H. Papadimitriou

UC Berkeley

www.cs.berkeley.edu/~christos

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


• 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?


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


• 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)


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)


Games, games…

randominformationset

strategies

strategies3,-2

payoffs


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


concepts of rationality

• undominated strategy

• Nash equilibrium

• randomized Nash equilibrium ( P?)

• perfect equilibrium

• subgame perfect equilibrium

• focal point


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)


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


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


• 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


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.


• 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


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]


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]


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!


price

quantity

q = a – b p

Example: market segmentation

Segment monopolistic market to maximize revenue

21SODA: January 8, 2001

or, in the a – b plane:

a

b

?Theorem: Optimumclustering is by linesthough the origin(hence: O(n ) DP)

2


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]

http://www.sims.berkeley.edu/~hal


• 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


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?

algorithms, games and the internet christos h. papadimitriou uc berkeley christos

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