Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois...
-
date post
21-Dec-2015 -
Category
Documents
-
view
214 -
download
0
Transcript of Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois...
![Page 1: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/1.jpg)
Economics and Computer Science
CS595, SB 213
Xiang-Yang Li Department of Computer Science
Illinois Institute of Technology
![Page 2: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/2.jpg)
Course information
Instructor: XiangYang Li [email protected], 312-567-5207, SB 237D
Homeworks?
Exams?
Projects?
Gradings?
![Page 3: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/3.jpg)
What is this course about
Using economics concept to solve some questions in computer science and vice versa
![Page 4: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/4.jpg)
What is economics?
What does economics study typically? Traditionally, business is follows
“Business is war” Outsmart the competition Capture the market share Make a killing brand Beating up supplies Locking up customers It is not enough to succeed. Others must fall.
![Page 5: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/5.jpg)
Nowadays
Doing business, we have to Listen to customers Work with suppliers Create teams Establish strategic partnerships
Even with competitors Business is not war,
You do not have to blow out the other fellow’s light to let your own shine!
but business is not peace either Battle with competitors over market share, fight
suppliers for cost,… What it is then?
![Page 6: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/6.jpg)
A new mindset
Business is Cooperation when it comes to creating
a big pie And competition when it comes to
divide it up! Have to compete and cooperate at the
same time To find a way bring together
competition and cooperation, we use Game theory
![Page 7: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/7.jpg)
What is computer science?
Algorithms and protocols to solve questions efficiently Algorithms
how to solve questions Programming language
tool to implement out ideas Architecture
way to build the machines to solve the questions Computer networking
way of exchange information Etc.
![Page 8: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/8.jpg)
What are assumptions of CS?
Traditionally Single computer, single user
So concentrate on efficiency, and cost Assume that the computing devices will
follow our protocols Computer networking
Still efficiency, and cost May consider fault tolerance, malicious
devices Thus, security is a issue
![Page 9: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/9.jpg)
Not always true
The network devices could be neither cooperative nor malicious Example: wireless networking Peer-to-peer computing grid computing
Computing devices and terminals belong to different users, and organizations Individual users are selfish Want to maximize its own benefit if possible
![Page 10: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/10.jpg)
Example: Wireless networks
No wired structure
Self-organized All nodes as
routers Broadcasted
signal Powered by
battery Scarce energy &
memory Mobile
![Page 11: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/11.jpg)
Selfish Users
How to model this? Turn to game theory
How to achieve a global system gold when selfish users are present? Economics results
How to implement this? Combine with cryptography and security
Is it efficient? Combine with traditional computer science
wisdoms
![Page 12: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/12.jpg)
The game view of business
Five basic elements of a game (PARTS) Players Added values Rules Tactics Scope
![Page 13: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/13.jpg)
Value Net
Company
customers
complementorscompetitors
suppliers
![Page 14: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/14.jpg)
Value Net
Complementor A player is your complementor if customers value
your product more when they have the other players product than they have your product alone.
Inter vs. Microsoft Competitor
A player is your complementor if customers value your product less when they have the other players product than they have your product alone.
Coca-cola vs. Pepsi-cola
![Page 15: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/15.jpg)
Game Theory
An example: Prof. Adam and 26 students Adam keeps 26 black cards and
distributes 26 red cards one to each student
Dean offer $100 for a pair of red and black cards
Restriction: students cannot gather together and bargain as a group with Adam.
What will each negotiation end up?50/50 split
![Page 16: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/16.jpg)
What happens if
Another example (Barry’s card game): Prof. Adam and 26 students Adam keeps 23 black cards and distributes
26 red cards one to each student Dean offer $100 for a pair of red and black
cards Restriction: students cannot gather
together and bargain as a group with Adam.
What will each negotiation end up?
Likely 90/10 split
![Page 17: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/17.jpg)
Added Value
Your added value= Size of the pie when you are in the game
minus the size of the pie when you are out of the game
Example Card game one
Added value of Adam is $2600, each student is $100, so total added value is $5200
Barry’s game Added value of Adam is $2300, each student is $0,
so total added value is $2300!
![Page 18: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/18.jpg)
What does it tell?
Instead of focusing on the minimum payoff you are willing to accept, be sure to consider how much the other players are willing to pay to have you in the game!
Do not confuse your individual added value with the larger added value of a group of people in the same position of the game as you Example: Barry’s card game
![Page 19: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/19.jpg)
Rules
Rules can change the game Card game example: Rule: take-it-or-leave-it negotiation: a
student can either accept or reject the offer by Adam, but not counter-offer, nor second offer from Adam.
What will the negotiation turn out to be? A 50/50 split or 90/10 split or something else Who is more powerful now?
![Page 20: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/20.jpg)
Rationality and Irrationality
Game theory assumes rational player Maximize its profits Understand the game No misperceptions No feelings of pride No fairness No jealousy, spite, vengefulness,
altruism But the world is not like this
So much for game theory,
![Page 21: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/21.jpg)
What is rationality
Rationality means A player is rational if he does the best
he can, given how he perceives the game, including his perceptions of perceptions, and how he evaluates the various possible outcomes of the game
A player can percept wrong and still be rational: he is doing the best he can given what he knows.
![Page 22: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/22.jpg)
Rationality as a Paradigm for
Internet Computing
Noam NisanHebrew University, Jerusalem
![Page 23: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/23.jpg)
Contents
The Internet and the new face of computing
Analyzing computing systems in equilibrium
Designing computational mechanisms
A defining problem: Combinatorial auctions
![Page 24: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/24.jpg)
What is Computing?
20th Century(second half)
21st century(first decade)
von Neumann Machine The Internet
![Page 25: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/25.jpg)
The Internet
• Huge dynamic heterogeneous distributed system – “normal distributed CS”
• Not centrally owned – different parts owned by different people, firms, or organizations with differing goals – “CS+economics+game-theory”’
![Page 26: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/26.jpg)
TCP Retransmission Rule
Transmission Control ProtocolUsed for most Internet communicationBreaks messages into packets, and
assembles the packets back into messagesHandles packet delay/loss
TCP Retransmission RuleWhen a packet is lost, decrease transmission rate (by a factor of 2)Rational: Network is congested – fix it by reducing demand down to capacity
![Page 27: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/27.jpg)
TCP Retransmission Rule
“Improved” Rule When a packet is lost, start sending each
packet twice Rational: Packets are lost – fix it by
increasing the probability that at least one copy of each packet arrives
Why not?
![Page 28: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/28.jpg)
Internet Resource Sharing The vision
everyone connected to the Internet should have access to all resources that are connected to the Internet
Examples: CPU-time Files I/O devices Data Knowledge Humans
Why share?
![Page 29: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/29.jpg)
Electronic Commerce
• How will computers talk business?
• Using communication, security software, agents, …
• Using standards: XML, .NET, J2EE, … and other TLAs
• What will they say to each other?
• “Book X costs Y”
• “Bid X for Y units of stock Z”
• “Here’s a complicated offer to you guys: @#$%^ ”
![Page 30: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/30.jpg)
Internet Computing Protocols
Should take into account Computational issues:
CPU time, communication, robustness, memory, languages, … Incentive issues:
Selfishness, strategies, payments, coalitions, risk, …
Should combine the points of view of Computer Science and of economics
Should apply game theory in a computational context
Rational behavior is more easily assumed from computers than from humans The strategy is in the software
![Page 31: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/31.jpg)
At All Protocol Levels …
eCommerce: eStores, auctions, exchanges, supply chains
Online Services: games, web-hosting, ASPs
Information Resources: music, databases
Computational resources: CPU, disk space, proxies, caching,
Network Infrastructure: routing, admission control, QoS
Low level (traditional CS domain)
High level (traditional business domain)
![Page 32: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/32.jpg)
The Price of Anarchy Take a “normal” CS protocol that works well
if everyone does what they should…. Say “Oh my god – the participating
computers may do whatever they want…” Analyze what happens when “they do
whatever they want” Radical departure from CS: “want” utility
rationality game-theory equilibrium Aim to prove that things are still not too bad Or else: argue against using on the Internet
![Page 33: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/33.jpg)
Minimizing Packet Delay Braess’s Paradox
1
1
x
x
0
delay proportionalto load
constant delay
• Many “small”packets – total quantity = 1
• Each knows the delay situation
• Each chooses how to get to destination
![Page 34: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/34.jpg)
Minimizing Packet Delay Braess’s Paradox
1
1
x
x
0
• Many “small”packets – total quantity = 1
• Each knows the delay situation
• Each chooses how to get to destination
Optimal routing (delay = 1.5)
1/2
0.5
0.5
1
1
1
10
Selfish routing (delay = 2.0)
![Page 35: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/35.jpg)
The Price of Anarchy is Low Roughgarden&Tardos
Theorem: for all network topologies, for all sets of routing requests, for all delay functions on the links:
1. If all delays are linear functions, then the previous example is as bad as it gets – the price of anarchy is at most a factor of 4/3 in delay
2. For general delay functions, doubling the edge capacities compensates for selfishness – the price of anarchy is at most a factor of 2 in infrastructure
![Page 36: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/36.jpg)
Algorithmic Mechanism Design Nisan&Ronen
Design the protocols so that they will work well under selfish behavior of participants
“work well” – the usual computational optimization goals “under selfish behavior” – the usual game-theoretic
concepts of equilibrium Use notions and techniques from the economic
field of Mechanism Design “Inverse game-theory”
Concentrate on “incentive compatibility” (truthfulness)
Equilibrium is reached when all players report their private information truthfully
The revelation principle shows that this is without loss of generality
![Page 37: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/37.jpg)
VCG-Mechanism in CS Vickrey-Clarke-Groves
Basic positive result in mechanism design Allow monetary transfers to/from
participants Basic idea: internalize externalities Each player pays/gets the total
loss/benefit in utility he causes to all others All players see the same goal: optimizing the total sum of players’ utilities
![Page 38: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/38.jpg)
VCG-Mechanism in CS Vickrey-Clarke-Groves
Shared Cache
Caching XXX will save me
100$
Caching XXX will save me 10$
Caching XXX will cost me 80$
Pay 70 (=80-10)Clarke tax
![Page 39: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/39.jpg)
Beyond Classical Mechanism
New domain of problems Parameter-complexity: e.g. structure of network Brave-new-world: disregard human conventions and biases
New optimization goals Not just sum-of-utilities: e.g. make-span in scheduling
New limitations Computational complexity Distributed implementation Interaction with usual mechanism design often problematic
New biases regarding solution concepts Computer scientists don’t like Bayesian analysis: real-world
distributions are too different from those in our analysis – worst-case will happen
Computer scientists are happy with approximations: optimality is often too hard
![Page 40: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/40.jpg)
Some Recent Results
Selling “digital goods” (unlimited supply) Goldberg&Hartline&Wright
A randomized mechanism can approximate monopoly price revenue Scheduling jobs on “unrelated machines” Nisan&Ronen
No better than 2-approximation for the make-span is possible, but randomized mechanisms can do better
Scheduling jobs on “related machines” Archer&Tardos
A polynomial time 3-approximation mechanism for the make-span Cost-sharing for multicast transmissions FPS
VCG mechanism can be implemented in linear communication Auctions using a few bits Blumrosen&Nisan
An auction with 1-bit from each player can achieve 98% efficiency
![Page 41: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/41.jpg)
Combinatorial Auctions
Most mechanism design problems involve resource allocation
The central problem in classical mechanism design is an auction: how to allocate a single indivisible good?
Abstracts many resource allocation problems English auction, Dutch auction, first price sealed-bid auction,
… Gold standard: Vickrey’s 2nd price auction
The emerging central problem in algorithmic mechanism design is a combinatorial auction: how to allocate a collection of goods, with complex dependencies between them?
Abstracts many complex resource allocation problems Involves a wide spectrum of computational and game-
theoretic issues
![Page 42: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/42.jpg)
Combinatorial Auction Problem
N indivisible non-identical items are sold concurrently
k bidders compete for subsets of these items Each bidder j has a valuation for each set of items:
vj(S) = value that j assigns to acquiring the set S vj is monotonic non-decreasing (“free disposal”)
Objective: Find a partition (S1…Sk) of {1..N} that maximizes the social welfare: j vj(Sj).
Means: protocol between bidders and auctioneer Difficulties: communication, computation,
incentives
![Page 43: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/43.jpg)
Complements and Substitutes
vj() may have complements: vj(ST) > vj(S)+vj(T) for some S and T. Extreme case: “single-minded bid” -- will
only pay for a complete package -- pay p for the set S but pay nothing for anything else
vj() may have substitutes: vj(ST) < vj(S)+vj(T) for some disjoint S and T. Extreme case: “unit demand bid” -- will pay
for at most a single item – the price may depend on the item
![Page 44: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/44.jpg)
Routing as Combinatorial Auction
Bidder A
Bidder B
Bidder C• Each bidder wants to buy some path to the destination
• Each link is an item
Destination
![Page 45: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/45.jpg)
The FCC Spectrum Auctions The FCC auctions spectrum licenses for many
geographic regions and various frequency bands
These auctions have raised billions of dollars The value of a license to a bidder depends on
the other licenses it holds Currently licenses are sold in a simultaneous auction USA Congress mandated that the next spectrum auction be made combinatorial.
3.1-3.2GHz
3.2-3.3GHz
3.3-3.4GHz
3.1-3.2GHz
3.2-3.3GHz
3.1-3.2GHz
3.2-3.3GHz
3.1-3.2GHz
3.2-3.3GHz
3.1-3.2GHz
3.2-3.3GHz
3.3-3.4GHz
![Page 46: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/46.jpg)
Basic Mechanism Approach Basic Solution
Each bidder sends vj() to auctioneer. Auctioneer finds the partition that maximizes j vj(Sj). Auctioneer allocates Sj to each bidder j Auctioneer charges VCG payments – ensures incentive
compatibility Computational difficulties
Bidding: How to send vj()? Requires communication of
numbers – impractical Allocation: How can the auctioneer find an optimal
allocation? The problem is computationally intractable (even to approximate well)
N2
![Page 47: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/47.jpg)
Bidding Languages The auction must fix a “language” for
representing valuations. All bidders will use that language to express their valuations
Language must be expressive: express all reasonable valuations succinctly
Language must be simple: computationally easy to manage valuations (represent, determine allocation,…)
Proposed languages use: package bids, OR, XOR (left-sock & right-sock : 5$) OR ( (Red-shirt : 10$) XOR (blue-shirt : 9$))
Different bidding languages have different power What should the FCC allow?
![Page 48: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/48.jpg)
Iterative AuctionsDefinition:
The demand of valuation v at item prices p1 … pn is the set S that maximizes the benefit: v(S)-i S pi
A Walrasian equilibrium is an allocation S1…Sm and item prices p1 … pn such that each Sj is the demand of vj at these prices
Fact: Any Walrasian equilibrium gives an optimal allocation
Algorithm: Demange&Gale&Sotomayor
initialize prices of all items to 0 repeat: if an item is demanded by more than one bidder, increase
the price a little; until a Walrasian equilibrium is reached
Theorem: This works if valuations are “gross substitutes” Kelso&Crawford
Theorem: In general, exponential communication (equivalently, an exponential number of prices) is needed Nisan&Segal
![Page 49: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/49.jpg)
Allocation Algorithms The allocation problem is computationally intractable Approaches for overcoming computational difficulty
Solve (or approximate) special tractable cases Gross substitutes Kelso&Crawford Sub-modular (2-approximation) Lehmann&Lehmann&Nisan Linear order on items Rothkopf&Pekec&Harstad
Heuristics that obtain optimal allocations and run “reasonable fast”
Practical for 100s of items CABOB -- Sandholm et al.
Heuristics that run quickly and find “reasonably good” solutions A few % loss for 1000s of items Zurel&Nisan
Use the usual tools of combinatorial optimization LP relaxation Branch-and-bound, cutting-planes Local search Dynamic programming
![Page 50: Economics and Computer Science CS595, SB 213 Xiang-Yang Li Department of Computer Science Illinois Institute of Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649d6a5503460f94a4967b/html5/thumbnails/50.jpg)
Incentives vs. Allocation Challenge: find a mechanism that obtains “reasonably
good” allocations and is computationally efficient. Key problem: Algorithms that find sub-optimal
allocations do not yield incentive compatible mechanisms Attaching VCG payments to sub-optimal algorithms essentially
never yields incentive compatibility Nisan&Ronen The only known incentive compatible mechanisms are VCG; for
“complete spaces” with at least 3 possible outcomes only VCG mechanisms exist. Roberts, Green&Laffont
Special case: single minded bidders – have a single valuation parameter and desire a single package
A Computationally efficient incentive compatible mechanism exists Lehmann&Ocallaghan&Shoham
Open problem: Find any non-VCG mechanism for any multi-dimensional valuation space