1. Pricing, Negotiation and Trust
Auction and Game Theory
ISP Web Algorithms:
November 8, 2002

2. Sources Osborne and Rubinstein A Course in Game Theory, MIT, 1994
Mas-Colell, Whinston, and Greene
Microeconomic Theory, Oxford, 1995
“these proceedings” survey
and …/focs01.ppt
ISP Web Algorithms:
November 8, 2002

3. The Internet
built, operated and used by a multitude of diverse economic interests
theoretical understanding urgently needed
tools: mathematical economics and game theory
ISP Web Algorithms:
November 8, 2002

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 router’s self-interest into account
ISP Web Algorithms:
November 8, 2002

5. E-trade on Internet
Economic efficiency in presence of selfish participants
ISP Web Algorithms:
November 8, 2002

6. Game Theory 3,-2 strategies strategies payoffs ISP Web Algorithms:
November 8, 2002

7. Prisoner Dilemma The length of prison term ISP Web Algorithms:
November 8, 2002

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!
ISP Web Algorithms:
November 8, 2002

9. e.g.
matching pennies
prisoner’s dilemma
1,-1
-1,1
-1,-1
-20,0
0,-20
-10,-10
auction
chicken 1 . n
1 … n
-1,-1
1,0
0,1
0,0
0, v – y
u – x, 0
ISP Web Algorithms:
November 8, 2002

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
Nash’s equilibrium: each participant chooses the best strategy,
given the strategy chosen by the other participant.
Two Nash equilibrium -- which one to choose?
ISP Web Algorithms:
November 8, 2002

11. Price Competition Example
No dominant strategy- Optimum price depends on other company’s price
One Nash’s equilibrium point
ISP Web Algorithms:
November 8, 2002

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. .
ISP Web Algorithms:
November 8, 2002

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
ISP Web Algorithms:
November 8, 2002

14. is it in P? Or Is it feasible to find the Nash’s fixed point
ISP Web Algorithms:
November 8, 2002

15. = 2 [Roughgarden and Tardos, 2000]
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?
ISP Web Algorithms:
November 8, 2002

16. Repeated prisoner’s dilemma? Herb Simon (1969): Bounded Rationality
More problems: Nash equilibria may be “politically incorrect:” Prisoner’s dilemma
Repeated prisoner’s 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 prisoner’s dilemma played by memory-limited players (e.g., automata)?
ISP Web Algorithms:
November 8, 2002

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 designer’s goals as dominating strategies
ISP Web Algorithms:
November 8, 2002

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
ISP Web Algorithms:
November 8, 2002

19. Theorem (The Revelation Principle): If there is a mechanism, then there is one in which all agents truthfully reveal their secret utilities.
ISP Web Algorithms:
November 8, 2002

20. but… these mechanisms are extremely complex and artificial
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
ISP Web Algorithms:
November 8, 2002

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
ISP Web Algorithms:
November 8, 2002

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.
ISP Web Algorithms:
November 8, 2002

23. e.g., shortest path auction3 6 5 s 4 t 6 10 3 11
pay e its declared cost c(e),
plus a bonus equal to dist(s,t)|c(e) = - dist(s,t)
ISP Web Algorithms:
November 8, 2002

24. Theorem: Resulting mechanism is truthful and maximizes social benefit
Theorem [Suri & Hershberger 01]: Payments can be computed by one shortest path computation.
ISP Web Algorithms:
November 8, 2002

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
ISP Web Algorithms:
November 8, 2002

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
ISP Web Algorithms:
November 8, 2002

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
ISP Web Algorithms:
November 8, 2002

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]
ISP Web Algorithms:
November 8, 2002

29. Game with players in [n] v (S) = the maximum total payoff
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?”
ISP Web Algorithms:
November 8, 2002

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 individual’s contribution when using personal data for decision-making
ISP Web Algorithms:
November 8, 2002

31. e.g., marketing survey [Kleinberg, Raghavan, P 2001]
company’s utility is proportional to the majority
customer’s utility is 1 if in the majority
how should all participants be compensated?
“likes”
customers
possible
versions of
product
ISP Web Algorithms:
November 8, 2002

32. the internet game
3, 2
capacity of the internal
network to carry traffic
(edges have  capacity)
1, 1
1, 4
2, 0
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
ISP Web Algorithms:
November 8, 2002

33. v[S] = 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?
ISP Web Algorithms:
November 8, 2002