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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

slide2

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

slide3
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

slide6
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

slide8

Games, games…

strategies

strategies

3,-2

payoffs

random

information

set

SODA: January 8, 2001

slide9

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

slide13

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

SODA: January 8, 2001

slide14

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

slide16

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

slide20

Example: market segmentation

quantity

Segment monopolistic market to maximize revenue

q = a – b  p

price

SODA: January 8, 2001

slide21

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

slide23

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

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