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

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

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

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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

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International Institute 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)

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

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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

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Some literature Miriam Herschlag and Rami Zwick Internet 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)

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

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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

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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

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Example instance 3 assets P,Q,R sequential English auction 5 bidders private valuation every bidder wants to purchase at most one asset

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Private valuations

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Nobody has information Winning bid Profit

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A knows valuations of B - E Reduced willingness to pay

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All have information about others valuations

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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

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Vickrey-Clarke-Groves auction scheme Every bidder x makes sealed bid p(x,s) for every asset s Auctioneer computes assignment with maximum revenue z max Price p*(x,s) to pay for bidder x for winning bid s: p*(x,s) = p(x,s) - (z max - z max (without x)) = z max (without x) - (z max - p(x,s))

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

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Comparison of results The Vickrey-Clarke-Groves design results in the same assignment at the same prices without requiring bidders to invest in getting information. But: Will all bidders reveal true valuation?

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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?

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Computation in our example: Bipartite Matching P Q R ED CBA 10 6 9 Rothkopf, Pekeč, Harstad (1998)

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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?

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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 can be assigned to bidders?

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Identical Assets: polynomial solvable Every bidder bids on numbers of assets: b ij 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.

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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.

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

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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

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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

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www.voetbalmarkt.nl www.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 with one share of each team Use the market to trade individual shares Note: market prices predict the outcome of the event

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A double auction - interface of the EURO 2000 market

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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?

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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?

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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

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

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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?

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