1. Algorithms, Games, and the Internet
S Kameshwaran
18 Oct, 2002

2. Refresh Equilibrium Concepts in Game Theory
Dominant Strategy Equilibrium
Dominant Strategy is the best strategy to any strategy played by other players
Combination of dominant strategy (one from each player) is a dominant strategy equilibrium
Nash Equilibrium
A strategy combination (one from each player) is a Nash equilibrium if each player’s strategy is a best response, given the other players’ strategies
Widely used

3. Refresh Mechanism Design Strategy-proof mechanisms
Truth-telling is the dominant strategy for each agent
Utilitarian Mechanisms: Maximize the sum of the valuations of all the players
VCG pricing mechanisms are strategy-proof for utilitarian mechanisms
VCG: Price an agent based on the inputs from the other agents
VCG: Not budget-balanced
Budget-balance is mandatory if there is in/out payments from/to agents (in payments >= out payments to avoid loss)

4. Refresh Mechanism Design Bayesian-Nash mechanisms
There exists a Bayesian-Nash equilibrium
Budget-balance is easy but to prove the existence of BNE may be difficult
Algorithmic concepts were only applied to strategy-proof mechanisms
No rigorous algorithmic mechanism design approach to Bayesian-Nash mechanisms

5. Algorithms, Games, and the Internet
Objective
To show that Game Theory and Mechanism Design are useful tools to model Internet mathematically, by focusing on the following applications
Interdomain Routing
CPU Marketplace
Web Caching
P2P File Sharing

6. Interdomain Routing
Internet is comprised of many separate administrative domains or autonomous systems (AS)
Routing of packets occurs at two levels:
Intradomain: route within single AS
Interdomain: route between AS
Currently handled by Border Gateway Protocol (BGP)

7. Interdomain Routing BGP
Used for carrying routing information between AS’s
Coveys information about AS topology
Path vector protocol
Node i stores, for each AS j, the lowest-cost AS path from i to j
Lowest-cost is in terms of number of hops
Each router sends its routing table to its neighbors, which based on this information calculate their own table
Routing table exchanges occur when a change is detected

8. Interdomain Routing BGP Model AS is considered as a node
N: Set of nodes (ASs), n=||N||
L: Set of bi-directional links in N, at most one link between two nodes
Tij: Intensity of traffic originating from i destined to j
ck: Per packet transit cost of node k
Transit traffic: Traffic neither originating from or destined for that AS
AS do not like to carry transit traffic
To compensate for cost each AS is paid a price

9. Interdomain Routing Objective
Minimize the total cost of routing all packets (Utilitarian)
AS that do not carry transit traffic pays nothing
Use BGP as the substrate
Straightforward extensions of existing protocols are easier to deploy than de novo designs
There is no central computation in BGP: Each node calculates its routing table and pass it on to its neighbors
Modifications to current BGP should not require new infrastructure in terms of computation and communication

10. Interdomain Routing
Algorithmic Mechanism Design (AMD)  Distributed Algorithmic Mechanism Design (DAMD)
Mechanism:
Optimization (Allocation)
Payments
AMD deals with the complexity of mechanism from a centralized system perspective
DAMD deals with the complexity of mechanism that is implemented across different systems
AMD  DAMD :: Algorithms  Distributed Algorithms

11. Interdomain Routing Strategy-proof pricing mechanism for routing
Payment to agent k for carrying transit traffic from i to j = ck (0 if it does not carry traffic) + [Transit cost of least cost path without k – Transit cost of least cost path with k]
Unique strategy-proof pricing scheme that belongs to VCG and guarantees no payment to node that carries no traffic

12. Interdomain Routing DAMD Mechanism using BGP
Least cost paths are calculated using ck instead of number of hops
Each node while sending the routing table information also sends its transit cost ck
Increases the standard BGP table by a constant factor
The local computation done at each AS is in the same order of magnitude of current BGP local computation time

13. Interdomain Routing
Conflict: AS as strategic agent and also as obedient computational system
Strategy-proof mechanisms were designed in order to avoid the AS lying about its true cost
For calculating the prices, the same AS were used
How can one be sure that would implement algorithm correctly?
It may modify the algorithm to its benefit
Verification systems might be possible solutions

14. Distributed task Allocation: CPU Marketplace
Computational Service Providers
Users with pervasive devices can offload CPU intensive jobs to the marketplace
Fixed pricing (like retail markets)
Dynamic Pricing (like auction markets, price is affected by the current demand)

15. CPU Marketplace One-sided Auction Model : Given: k tasks
Agents: n computational facilities (bidders, reverse auction)
Agent i’s type: tij, minimum amount of time required by agent i to complete job j (private information)
xi: Set of tasks allocated to agent i
Agent i’s valuation: -jxitij
Goal of the Market: mini jxitij (Minimize the makespan)

16. CPU Marketplace MinWork approximation Makespan: MinWork Mechanism
mini jxitij <= j mini tij
mini jxitij >= (1/n) j mini tij
MinWork Mechanism
Utilitarian: j mini tij (Reverse Auction, the valuations are negative: min instead of max)
Payment: Agent is given the payment equal to the second best agent for this task
VCG Mechanism: Strategy-proof
Equivalent to auctioning each task separately in a Vickrey Auction

17. CPU Marketplace
Is there any other better strategy-proof approximation mechanism?
Users with tasks pay the agents
What if the users are charged more than they can pay?
Use of reserve prices: users have reserve prices and they cannot pay more than that
Devise a strategy-proof approximation mechanism with reserve prices

18. CPU Marketplace Double Auction:
Sellers: CPU providers (computational facility)
Buyers: Users (Tasks)
Budget-Balance is mandatory: Payment to sellers is made from the payments collected from the buyers
Devise a Bayesian-Nash Mechanism that is budget-balanced and efficient

19. Web Caching Web caches enhance performance of web access
Eliminate hot spots in the network
Reduce access latencies
Web-caching Architecture (Current):
Set of collaborating caches to interact and serve a client community
Intent: To achieve overall system efficiency
Assumption: Caches are obedient

20. Web Caching
What if the architecture spans different administrative boundaries?
Two incentive issues:
Clients reporting to a single cache
Caches reporting to the architecture

21. Web Caching Single Cache in isolation
Maximize the utility of requesting clients
Caching the frequently requested pages that provide the highest user utility
Utility are private information to the clients
What are the strategy-proof mechanisms that can elicit truthful valuations from clients?

22. Web Caching Collaboration among caches
Caches incur cost for storing a page
If there is no monetary transfer, caches may manipulate other caches to store pages
If there is monetary gain, then caches might “compete” to serve highest-value pages and thereby duplicating content: sub-optimal performance
Design a mechanism that can distribute the caching load among caches such that performance is maximized
Devise a mechanism for web caching architecture where clients are induced to report their true values to the caches and caches are induced to implement optimal resource allocation

23. Peer-to-Peer File Sharing
P2P
Sharing of files: original work, public domain works, publicly shared works
Gnutella, Freenet, KaZaA
Autonomous Distributed Systems
Each machine belongs to a different user
No central administrative authority
Gift Economy
Users offer content, access bandwidth, storage, CPU for free

24. Peer-to-Peer File Sharing
Interacting Messages
Ping: “Are you there?”: Directed at a Peer
Pong: “Yes, I am here”
Query: “I am looking for 007 posters”
Query Response: “I have the poster. Download from xxx.xxx.xxx.xxx:xx
All these messages are forwarded from a Peer to its neighbors

25. Peer-to-Peer File Sharing
Free Rider Problem
No individual is willing to contribute towards the cost of something (public goods) when he hopes that someone else will bear the cost instead
Everybody in a block of flats may want a faulty light repaired, but no one wants to bear the cost of organizing the repair themselves
In P2P, many people just download files contributed by others and never share any of their files
Files shared in P2P are ‘public goods’
Free Rider Statistics in Gnutella: 70% of users share no files
Few servers become the hot spots: Anonymous?, Copyright?, Privacy? Is it P2P?

26. Peer-to-Peer File Sharing
Gift Economy  Barter Economy
MojoNation P2P
Awarding “Mojo” for offering resources
“Mojo” is exchanged to gain priority access when is system is overloaded
What are the performance characteristics of the equilibria that result from barter P2P systems?

27. Peer-to-Peer File Sharing
Barter Economy  Monetary Economy??
Money exchange
Can one design monetary P2P systems that provide better performance than barter P2P systems?
Incentive Issues of Peers: Caching + Routing
Caches: Storing shared files
Routers: Routing query and other messages
How to model these incentive issues in P2P systems?

28. References
Algorithmic Mechanism Design, Noam Nisan and Amir Ronen, 2001
Distributed Algorithmic Mechanism Design: Recent Results and Future Directions, Joan Feigenbaum and Scott Shenker, 2002
A BGP-based Mechanism for Lowest Cost Routing, Joan Feigenbaum, Christos Papadimitriou, Rahul Sami, and Scott Shenker, 2002
Algorithms, Games, and the Internet, Christos Papadimitriou, 2001

29. 22/10/02 (Tuesday): Constraint Satisfaction Problems and Games
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22/10/02 (Tuesday): Constraint Satisfaction Problems and Games