Slide 1 of 27Noam Nisan

Rationality as a Paradigm for

Internet Computing

Noam NisanHebrew University, Jerusalem

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Contents

• The Internet and the new face of computing• Analyzing computing systems in equilibrium • Designing computational mechanisms• A defining problem: Combinatorial auctions

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What is Computing?

20th Century(second half)

21st century(first decade)

von Neumann Machine The Internet

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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”’

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TCP Retransmission Rule

• Transmission Control Protocol Used for most Internet communication Breaks messages into packets, and assembles the packets back into messages Handles packet delay/loss

• TCP Retransmission Rule When a packet is lost, decrease transmission rate (by a factor

of 2) Rational: Network is congested – fix it by reducing demand

down to capacity

• “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?

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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?

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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: @#$%^ ”

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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

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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)

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The Price of Anarchy Papadimitriou

• 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

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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

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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)

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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

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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

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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

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

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Beyond Classical Mechanism Design

• 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

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A Sampling of 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

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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

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Combinatorial Auction Problem Definition

• 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

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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

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Routing as a Combinatorial Auction

Bidder A

Bidder B

Bidder C• Each bidder wants to buy some path to the destination

• Each link is an item

Destination

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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

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Basic Mechanism Design 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

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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?

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Iterative Auctions

Definition: 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

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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

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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