The New Economy – auctions as mechanism and content for the Web

1. The New Economy –auctions as mechanism and content for the Web Rudolf Müller International Institute of Infonomics rudolf.muller@infonomics.nl

2. Joint work with • Stan van Hoesel, University Maastricht • Jan Hansen, HU Berlin • Carsten Schmidt, HU Berlin • Martin Strobel, HU Berlin

3. Outline • About Infonomics • Auctions - mechanism and content • Auctions as a mechanism • Internet auctions • Multi-item auctions • Auctions as content • event markets • Summary

4. New science of Infonomics • analyses the impact of digitization of information on: • individual and collective behavior • learning, cognitive patterns and competence development • organizational and economic structure and performance • ethical norms and values and the legal system • knowledge accumulation and diffusion • communication modes, democracy, culture

5. InternationalInstitute of Infonomics • Interdisciplinary research institute • Director Luc Soete • Research tracks • e-basics (Paul Windrum, Rishab Ghosh) • e-behavior (Rita Walczuch) • e-organization (Rudolf Müller) • e-society (Huub Meijers) • e-content (Jan Bierhoff)

6. Auctions - Mechanism and Content • E-commerce changes traditional mechanisms • lower transaction costs • more interactivity, more knowledge • new intermediaries • Auctions are a good example

7. Auctions - Mechanism and Content • E-commerce invents new content • totally digital products and services • almost zero cost for additional copy • high network externalities • Auctions are a good example

8. Some literature • Miriam Herschlag and Rami ZwickInternet Auctions - Popular and Professional Literature Review, WWW (1999) • Agorics, Inc. Auctions. Going, Going, Gone! A Survey of Auction Types, WWW (2000) • Sven de Vries and Rakesh Vohra, Combinatorial Auctions: A Survey, from the authors (2000) • Rudolf Müller and Stan van Hoesel, Optimization in Electronic Markets - Examples from Combinatorial Auctions, Netnomics (2000)

9. open, increasing bid: English auction open, decreasing bid:Dutch auction closed, second price: Vickrey Auction closed, highest price:discriminating auction Auctions -Mechanism Four standard formats

10. Internet Auctions • Private to private auctions • successful format • customer satisfaction is a problem • Business to consumer • popular live auctions • Business to business • in particular for perishable goods • format: multi-item

11. Multi-item auctions • Bidders observe (dis-)economies of scale: valuation of a set of assets is smaller or larger than the sum of the valuations • Problems if assets are auctioned independently: threshold problem, exposure problem, efficiency, optimality • Widely discussed in the context of frequency auctions

12. Example instance • 3 assets P,Q,R • sequential English auction • 5 bidders • private valuation • every bidder wants to purchase atmost one asset

13. Private valuations

14. Nobody has information Winning bid Profit

15. A knows valuations of B - E Reduced willingness to pay

16. All have information about others valuations

17. General case • bidders have knowledge about distribution of other bidders valuation • bidders bid less in order to maximize expected return • costs for getting information reduce the expected profit

18. Vickrey-Clarke-Grovesauction scheme • Every bidder x makes sealed bid p(x,s) for every asset s • Auctioneer computes assignment with maximum revenue zmax • Price p*(x,s) to pay for bidder x for winning bid s:p*(x,s) = p(x,s) - (zmax - zmax(without x)) = zmax(without x) - (zmax - p(x,s))

19. Result in our example Assume: A, B, C, D, E bid their valuation Winner: C(P), B(Q), A(R) Price that C has to pay: Rev. without C 20 - Revenue from other bids -14 To pay 6

20. Comparison of results • The Vickrey-Clarke-Groves design results in the same assignment at the same prices withoutrequiring bidders to invest in getting information. • But: Will all bidders reveal true valuation?

21. Valuation revealing • Theorem (Clarke 1971, Groves 1973)Revealing true valuation is a dominant strategy • But: how are the winning bids and their prices computed by the auctioneer?

22. Computation in our example:Bipartite Matching A B C D E 10 6 9 Q P R Rothkopf, Pekeč, Harstad (1998)

23. Algorithmic questions for combinatorial bids • Does there exist a polynomial time algorithm to solve the winner assignment, or is the problem NP-hard? • If it is NP-hard, does additional structure make it polynomial solvable? • If it is hard, can a smart algorithm solve the problem in reasonable time?

24. 3-dim matching is a combinatiorial auction Left nodes are the bidders, they bid 1 $ on grey and blue nodes covered by the triangles. How many bids canbe assigned to bidders?

25. Identical Assets:polynomial solvable Every bidder bids on numbers of assets: bij price by bidder i for j assets. Let m(i,s) be the value of the optimal assignment if bids by bidders 1,…,i are considered and at most s assets are assigned.

26. Linearly ordered assets Bidders bid on sets of neighboured assets Polynomial solvable if we allow to assign more than one bid per bidder (Rothkopf et al.) Complexity unknown, if we allow to assign at most one bid to every bidder.

27. Integer linear programming test results Linear instances are much easier to solve. Medium sized random instances are solvable.

28. Related Research • Gomber, Schmidt, Weinhardt, Efficiency, incentives and computational tractability in MAS-Coordination • Rothkopf, Pekec, Harstad, Computationally manageable combinational auctions • Sandholm, An algorithm for optimal winner determination in combinatorial auctions • Andersson, Tenhune, Ygge, Integer Programming for Combinatorial Auction Winner Determination • Fujishima, Leyton-Brown and Shohan, Taming the computational complexity of combinatorial auctions

29. Auctions as content:Trading event bets • Customers buy and sell shares that represent events in a virtual stock market • Final price depends on outcome of event • Example: election markets in the US. Final price = percentage of a political party at the election • Example: EURO 2000 market

30. www.voetbalmarkt.nlwww.fussballmarkt.de • Example event: England – Germany • Three types of shares: E wins, G wins, draw • Value after the game: 1000 if event true • Participants buy bundles at price 1000 withone share of each team • Use the market to trade individual shares • Note: market prices predict the outcome of the event

31. A double auction - interface of the EURO 2000 market

32. Information processing in event markets • A stock market is able to translate information of traders into market prices • Applications: • Auctions on events inside a company: when will a project be completed? • Auctions on new products: what market share can a product gain?

33. Research questions • How efficient is information translated (in election markets small parties are overpriced)? • How does the market influence the opinion of a trader? • Is it legal to do such auctions via the Internet?

34. Summary • Auctions provide mechanisms and content in the New Economy • Auction mechanisms challenge game theory, operations research and experimental economics • Event trading provides content and testbed for experimental economics

35. Integer linear programming x i,j = 1 if bidder i is assigned set Sij, 0 else.

36. Complexity: Node packing is a combinatorial auction Every node is willing to pay 1 $ for its adjacent edges. How many nodes can be assigned a bid?