Download Algorithms, Games, and the Internet

Algorithms, Games, and the
Internet
S Kameshwaran
18 Oct, 2002
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 Equilibrium Concepts in Game Theory
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Dominant Strategy Equilibrium
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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
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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
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 Mechanism Design
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Strategy-proof mechanisms
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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)
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 Mechanism Design
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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 strategyproof mechanisms
 No rigorous algorithmic mechanism design
approach to Bayesian-Nash mechanisms
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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
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Interdomain Routing
 CPU Marketplace
 Web Caching
 P2P File Sharing
Interdomain Routing
 Internet is comprised of many separate
administrative domains or autonomous
systems (AS)
 Routing of packets occurs at two levels:
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Intradomain: route within single AS
Interdomain: route between AS
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Currently handled by Border Gateway Protocol (BGP)
Interdomain Routing
 BGP
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Used for carrying routing information between AS’s
Coveys information about AS topology
Path vector protocol
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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
Interdomain Routing
 BGP Model
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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
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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
Interdomain Routing
 Objective
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Minimize the total cost of routing all packets (Utilitarian)
AS that do not carry transit traffic pays nothing
Use BGP as the substrate
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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
Interdomain Routing
 Algorithmic Mechanism Design (AMD)  Distributed
Algorithmic Mechanism Design (DAMD)
 Mechanism:
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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
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AMD  DAMD :: Algorithms  Distributed
Algorithms
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
Interdomain Routing
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DAMD Mechanism using BGP
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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
Interdomain Routing
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Conflict: AS as strategic agent and also as
obedient computational system
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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
Distributed task Allocation:
CPU Marketplace
 CPU Marketplace
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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)
CPU Marketplace
 One-sided Auction Model :
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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)
CPU Marketplace
 MinWork approximation Makespan:
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mini jxitij <= j mini tij
mini jxitij >= (1/n) j mini tij
 MinWork Mechanism
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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
CPU Marketplace
 Is there any other better strategy-proof
approximation mechanism?
 Users with tasks pay the agents
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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
CPU Marketplace
 Double Auction:
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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
Web Caching
 Web caches enhance performance of web access
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Eliminate hot spots in the network
Reduce access latencies
 Web-caching Architecture (Current):
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Set of collaborating caches to interact and serve a client
community
Intent: To achieve overall system efficiency
Assumption: Caches are obedient
Web Caching
 What if the architecture spans different
administrative boundaries?
 Two incentive issues:
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Clients reporting to a single cache
Caches reporting to the architecture
Web Caching
 Single Cache in isolation
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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?
Web Caching
 Collaboration among caches
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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
Peer-to-Peer File Sharing
 P2P
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Sharing of files: original work, public domain works,
publicly shared works
Gnutella, Freenet, KaZaA
Autonomous Distributed Systems
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Each machine belongs to a different user
No central administrative authority
Gift Economy
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Users offer content, access bandwidth, storage, CPU for free
Peer-to-Peer File Sharing
 Interacting Messages
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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
Peer-to-Peer File Sharing
 Free Rider Problem
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No individual is willing to contribute towards the cost of
something (public goods) when he hopes that someone
else will bear the cost instead
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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
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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?
Peer-to-Peer File Sharing
 Gift Economy  Barter Economy
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MojoNation P2P
Awarding “Mojo” for offering resources
 “Mojo” is exchanged to gain priority access when is
system is overloaded
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 What are the performance
characteristics of the equilibria that
result from barter P2P systems?
Peer-to-Peer File Sharing
 Barter Economy  Monetary Economy??
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Money exchange
Can one design monetary P2P systems that provide
better performance than barter P2P systems?
 Incentive Issues of Peers: Caching + Routing
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Caches: Storing shared files
Routers: Routing query and other messages
 How to model these incentive issues in P2P
systems?
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
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22/10/02 (Tuesday): Constraint Satisfaction
Problems and Games