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Algorithms, Games and the Internet

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### Algorithms, Gamesand the Internet

Christos H. Papadimitriou

UC Berkeley

www.cs.berkeley.edu/~christos

- “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

- 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

- 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

- 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

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

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

- 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]

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

- 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

- 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:

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

- 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

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:

- 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 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

quantity

Segment monopolistic market to maximize revenue

q = a – b p

price

SODA: January 8, 2001

b

Theorem: Optimum

clustering is by lines

though the origin

(hence: O(n ) DP)

?

2

a

SODA: January 8, 2001

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

- 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]

“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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