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Algorithms, Games and the Internet. Christos H. Papadimitriou UC Berkeley www.cs.berkeley.edu/~christos. Outline. “new” vs. “old theory” Game Theory pricing multicast content the price of anarchy the economics of clustering the economics of privacy.

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Algorithms games and the internet

Algorithms, Gamesand the Internet

Christos H. Papadimitriou

UC Berkeley

www.cs.berkeley.edu/~christos


Algorithms games and the internet

Outline

  • “new” vs. “old theory”

  • Game Theory

  • pricing multicast content

  • the price of anarchy

  • the economics of clustering

  • the economics of privacy

SODA: January 8, 2001


Algorithms games and the internet

  • 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?

SODA: January 8, 2001



The internet
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

SODA: January 8, 2001


Algorithms games and the internet

  • new math for the new Theory?

    cf: George Boole The Laws of Thought, 1854

    Part I: propositional logic, Part II:probability

    cf: John von Neumann The Report on EDVAC, 1945

    Theory of Games and Economic Behavior, 1944

    (cf: Alan Turing On Computable Numbers, 1936

    Studies in Quantum Mechanics, 1932-35)

SODA: January 8, 2001


Game theory
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)

SODA: January 8, 2001


Algorithms games and the internet

Games, games…

strategies

strategies

3,-2

payoffs

random

information

set

SODA: January 8, 2001


Algorithms games and the internet

matching pennies

prisoner’s dilemma

auction

chicken

0, v – y

u – x, 0

SODA: January 8, 2001


Concepts of rationality
concepts of rationality

  • undominated strategy

  • Nash equilibrium

  • randomized Nash equilibrium (  P?)

  • perfect equilibrium

  • subgame perfect equilibrium

  • focal point

SODA: January 8, 2001


Some current areas of algorithmic interest
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)

SODA: January 8, 2001


E g pricing multicasts feigenbaum p shenker stoc2000
e.g., pricing multicasts [Feigenbaum, P., Shenker, STOC2000]

52

30

costs

{}

21

21

40

70

{11, 10, 9, 9}

{14, 8}

{9, 5, 5, 3}

32

{23, 17, 14, 9}

{17, 10}

utilities of agents in the node

(u = the intrinsic value of the information

agent i, known only to agent i)

i

SODA: January 8, 2001


Algorithms games and the internet

i

i

SODA: January 8, 2001


Algorithms games and the internet

  • 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

i

i

i

u 

i

def

i

i

i

i

i

i

i

1

n

1

i

n

  • budget balance

  •  v = c ( T [x])

  • Shapley mechanism

i

i

SODA: January 8, 2001


Our contribution
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.

SODA: January 8, 2001


Algorithms games and the internet

  • 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

i

i

i

u 

i

def

i

i

i

i

i

i

i

1

n

1

i

n

  • budget balance

  •  v = c ( T [x])

  • Shapley mechanism

i

i

SODA: January 8, 2001


Bounding nash equilibria the price of anarchy
Bounding Nash equilibria: the price of anarchy

cost of worst Nash equilibrium

“socially optimum” cost

s

t

3/2 [Koutsoupias and P, 1998]

general

multicommodity

network

2 [Roughgarden and Tardos, 2000]

SODA: January 8, 2001


Some interesting directions
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]

SODA: January 8, 2001


The economics of clustering
The economics of clustering

  • The practice of clustering: Confusion, too many criteria and heuristics, no guidelines

  • The theory of clustering: ditto!

  • “It’s the economy, stupid!”

  • [Kleinberg, P., Raghavan STOC 98, JDKD 99]

SODA: January 8, 2001


Algorithms games and the internet

Example: market segmentation

quantity

Segment monopolistic market to maximize revenue

q = a – b  p

price

SODA: January 8, 2001


Algorithms games and the internet

or, in the a – b plane:

b

Theorem: Optimum

clustering is by lines

though the origin

(hence: O(n ) DP)

?

2

a

SODA: January 8, 2001


On privacy
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]

SODA: January 8, 2001


Algorithms games and the internet

some thoughts on privacy

  • 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

SODA: January 8, 2001


E g marketing survey with kleinberg and raghavan
e.g., marketing survey [with Kleinberg and Raghavan]

“likes”

  • company’s utility is proportional to the majority

  • customer’s utility is 1 if in the majority

  • how should all participants be compensated?

customers

possible

products

SODA: January 8, 2001