Rationality as a Paradigm for Internet Computing

1. Rationality as a Paradigm forInternet Computing Noam Nisan Hebrew University, Jerusalem

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

3. 20th Century (second half) 21st century (first decade) What is Computing? The Internet von Neumann Machine

4. 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”’

5. 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?

6. 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?

7. 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: @#$%^ ”

8. 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

9. At All Protocol Levels … High level (traditional business domain) • 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)

10. 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

11. Minimizing Packet DelayBraess’s Paradox constant delay delay proportional to load x 1 0 1 x • Many “small”packets – total quantity = 1 • Each knows the delay situation • Each chooses how to get to destination

12. Minimizing Packet DelayBraess’s Paradox 1 0.5 1 0.5 1/2 x 1 Optimal routing (delay = 1.5) 0 1 x 1 • Many “small”packets – total quantity = 1 • Each knows the delay situation • Each chooses how to get to destination 0 1 Selfish routing (delay = 2.0)

13. 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: • 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 • For general delay functions, doubling the edge capacities compensates for selfishness – the price of anarchy is at most a factor of 2 in infrastructure

14. Algorithmic Mechanism DesignNisan&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

15. 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 Pay 70 (=80-10) Clarke tax Caching XXX will save me 100$ Shared Cache Caching XXX will cost me 80$ Caching XXX will save me 10$

16. 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

17. 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

18. 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

19. 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 • vjis monotonic non-decreasing (“free disposal”) • Objective: Find a partition (S1…Sk) of {1..N} that maximizes the social welfare: jvj(Sj). • Means: protocol between bidders and auctioneer • Difficulties: communication, computation, incentives

20. Complements and Substitutes • vj() may have complements: vj(ST) > 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(ST) < 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

21. Routing as a Combinatorial Auction Bidder A Destination Bidder B Bidder C • Each bidder wants to buy some path to the destination • Each link is an item

22. 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 3.1-3.2GHz 3.2-3.3GHz 3.2-3.3GHz 3.3-3.4GHz 3.1-3.2GHz 3.2-3.3GHz 3.1-3.2GHz 3.1-3.2GHz 3.2-3.3GHz 3.2-3.3GHz 3.3-3.4GHz

23. Basic Mechanism Design Approach • Basic Solution • Each bidder sendsvj() to auctioneer. • Auctioneer finds the partition that maximizes jvj(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)

24. 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?

25. Iterative Auctions Definition: • The demand of valuation v at item prices p1 … pnis the set S that maximizes the benefit: v(S)-iSpi • A Walrasian equilibrium is an allocation S1…Sm and item prices p1 … pnsuch 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

26. 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

27. 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