November 8, 2002

1
Pricing, Negotiation and Trust

• Auction and Game Theory

2
Sources

• Osborne and Rubinstein A Course in Game Theory,
  MIT, 1994
• Mas-Colell, Whinston, and Greene
• Microeconomic Theory, Oxford, 1995
• these proceedings survey
• http//www.cs.berkeley.edu/christos/games/cs294.h
  tml and /focs01.ppt

3
The Internet

• built, operated and used by a multitude of
  diverse economic interests
• theoretical understanding urgently needed
• tools mathematical economics and game theory

4
Routing on Internet

• So far voluntary
• In future Huge amount of data transferred (e.g.
  video)
• bandwidth reservation for QoS
• altruism may not persit.
• May need to design protocols taking routers
  self-interest into account

5
E-trade on Internet

• Economic efficiency in presence of selfish
  participants

6
Game Theory
strategies
strategies
3,-2
payoffs
7
Prisoner Dilemma

• The length of prison term

8
How to solve this game?

• What strategies are "rational" if both men want
  to minimize the time they spend in jail?
• Al reasoning
• "Two things can happen
• (case 1) Bob cheat
• Then Al get 20 years if he does not cheat
• 10 years if he cheats
• Al best to cheat.
• (case 2) Bob keep quiet
• If Al quiet, Al gets a year
• If Al cheat, Al goes free.
• Either way, it's best Al cheat.
• Therefore, Al should cheat
• Is it the best strategy? No! if both quiet,
  only one year in prison!

9
matching pennies
prisoners dilemma
e.g.
auction
chicken
0, v y
u x, 0
10
Information Technology Example
Choosing Information Systems Payoff matrix

• Observation must have compatible standard in
  order to work together
• No dominating strategy -- best one depends on
  other player
• Nashs equilibrium each participant chooses
  the best strategy,
• given the strategy chosen by the other
  participant.
• Two Nash equilibrium -- which one to choose?

11
Price Competition Example

• No dominant strategy- Optimum price depends on
  other companys price
• One Nashs equilibrium point

12
Concepts of rationality

• undominated strategy
• (problem too weak)
• (weakly) dominating srategy (alias duh?)
• (problem too strong, rarely exists)
• Nash equilibrium (or double best response)
• (problem may not exist)
• Randomized Nash equilibrium
• Theorem Nash 1952 Nash equilibrium Always
  exists.

. . .
13
The critique of mixed Nash

• Is it really rational to randomize?
• (cf bluffing in poker, IRS audits)
• There may be too many Nash equilibria

14
is it in P?Or Is it feasible to find the Nashs
fixed point
15
The price of anarchy
cost of worst Nash equilibrium
Koutsoupias and P, 1998
socially optimum cost
routing in networks
2 Roughgarden and Tardos, 2000
The price of the Internet architecture?
16

• More problems Nash equilibria may be
  politically incorrect Prisoners dilemma
• Repeated prisoners dilemma?
• Herb Simon (1969) Bounded Rationality
• the implicit assumption that reasoning and
• computation are infinitely cheap
• is often at the root of negative results in
  Economics
• Idea Repeated prisoners dilemma played by
  memory-limited players (e.g., automata)?

17
Mechanism design(or inverse game theory)

• agents have utilities but these utilities are
  known only to them
• game designer prefers certain outcomes depending
  on players utilities
• designed game (mechanism) has designers goals as
  dominating strategies

18
Mechanism design (math)

• n players, set K of outcomes, for each player i a
  possible set Ui of utilities of the form u K ?
  R
• designer preferences P U1 ? ? Un ? 2K
• mechanism strategy spaces Si, plus a mapping G
  S1 ? ? Sn ? K

19
Theorem (The Revelation Principle) If there is
a mechanism, then there is one in which all
agents truthfully reveal their secret utilities.
20

• but if we allow mechanisms that use Nash
  equilibria instead of dominance, then almost
  anything is implementable
• but these mechanisms are extremely complex and
  artificial

21

• but if outcomes in K include payments (K K0 ?
  Rn ) and utilities are quasi-linear (utility of
  core outcome plus payment) and designer prefers
  to optimize the sum of core utilities, then the
  Vickrey-Clarke-Groves mechanism works

22
e.g., Vickrey auction

• Sealed-highest-bid auction encourages gaming and
  speculation
• Vickrey auction Highest bidder wins,
• pays second-highest bid
• Theorem Vickrey auction is a truthful
  mechanism.
• Theorem It maximizes social benefit and
  auctioneer expected revenue.

23
e.g., shortest path auction
3
6
5
4
t
s
6
10
3
11
pay e its declared cost c(e), plus a bonus equal
to dist(s,t)c(e) ?- dist(s,t)
24

• Theorem Resulting mechanism is truthful and
  maximizes social benefit
• Theorem Suri Hershberger 01 Payments can
  be computed by one shortest path computation.

25
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 to
agent i, known only to agent i)
i
26

• 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 rules

i
i
27
Algorithmic Mechanism Design

• central problem
• few results outside social welfare maximization
  framework (n.b.Archer and Tardos 01)
• VCG mechanism often breaks the bank
• approximation rarely a remedy (n.b.Nisan and
  Ronen 99, Jain and Vazirani 01)
• wide open, radical departure needed

28
Algorithmic aspects of auctions

• Optimal auction design Ronen 01
• Combinatorial auctions Nisan 00
• Auctions for digital goods
• On-line auctions
• Communication complexity of combinatorial
  auctions Nisan 01

29
Coalitional games
Game with players in n v (S) the maximum
total payoff of all players in S,
under worst case play by n
S How to split v (n) fairly?
30
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 evaluate the individuals contribution
  when using personal data for decision-making

31
e.g., marketing survey Kleinberg, Raghavan, P
2001

• companys utility is proportional to the
  majority
• customers utility is 1 if in the majority
• how should all participants be compensated?

likes
customers
possible versions of product
32
the internet game
3, 2
capacity of the internal network to carry
traffic (edges have ? capacity)
1, 1
2, 0
1, 4
5, 9
3, 1
intensity of traffic to/from this
node, distributed to other nodes
proportionately to their intensity
3, 6
2, 2
7, 4
3, 1
33
vS value of total flow that can be
handled by the subgraph induced by S

• Compute the Shapley flow
• Find a flow in the core
• Under what circumstances is the core
• nonempty? Contains all maximal flows?