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Pricing and Bidding Strategies in Iterative Combinatorial Auctions

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Pricing and Bidding Strategies in Iterative Combinatorial Auctions Institut f¨urInformatik der Technischen Universit¨atM¨unchen Lehrstuhl f¨urInformatik XVIII Pricing and Bidding Strategies in Iterative Combinatorial Auctions Alexander Pikovsky Vollst¨andiger Abdruck der von der Fakult¨atf¨urInformatik der Technischen Universit¨at M¨unchen zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzender: Univ.-Prof. Michael Beetz, Ph.D. Pr¨uferder Dissertation: 1. Univ.-Prof. Dr. Martin Bichler 2. Univ.-Prof. Alfons Kemper, Ph.D. Die Dissertation wurde am 30.01.2008 bei der Technischen Universit¨at M¨unchen eingereicht und durch die Fakult¨atf¨urInformatik am 07.07.2008 angenommen. For Vita Pikovskaya Abstract Auctions have been getting increasing attention in computer science and eco- nomics, as they provide an efficient solution to resource allocation problems with self-interested agents. E-Commerce and finance have emerged as some of their largest application fields. The need for new auction mechanisms that allow for complex bids such as bundle bids and multi-attribute bids has been raised in many situations. In addition to strategic problems, the design of these multidimensional auctions exhibits hard computational problems. For example, the winner determination typically leads to NP-hard allocation prob- lems in combinatorial auctions. More recently, researchers have focused on the pricing and information feedback in combinatorial auctions. Iterative combinatorial auctions (ICAs) are IT-based economic mechanisms in which bidders submit bundle bids iteratively and the auctioneer computes allocations and ask prices in each auction round. Several ICA designs have been proposed in the literature, but very little was known about their behavior in different settings. The multi-item and discrete nature of ICAs and complex auction rules defy much of the traditional game theoretical analysis in this field. The literature provides merely equilibrium analysis of ICAs with non- linear personalized prices under strong assumptions on bidders’ strategies. In contrast, ICAs based on linear prices have performed very well in the lab and in the field. Computational methods and laboratory experiments can be of great help in i ii exploring potential auction designs and analyzing the virtues of various design options. The goal of our research was to benchmark different existing ICA designs and to propose new, improved auction rules. We focused on linear- price auctions, but also included one ICA design with non-linear personalized prices. In the computational simulations we compared three selected linear price ICA designs and the VCG auction based on the allocative efficiency, revenue distri- bution, and speed of convergence using different bidding strategies and bidder valuations. We found that ICA designs with linear prices performed very well for different value models even in case of high synergies among the valuations. There were, however, significant differences in the efficiency and revenue dis- tribution of the three ICA designs. Even heuristic bidding strategies in which bidders submit bids for only a few of the best bundles led to high levels of efficiency. We have also identified a number of auction rules for the ask price calculation, bidder activity, and auction termination that have shown to per- form very well in the simulations. In the laboratory experiments we compared the same auction designs and one ICA design with non-linear personalized prices in respect to the same perfor- mance measures. We were able to identify several similarities to the compu- tational results, but also quite heterogeneous bidding behavior, which did not correspond to the pure myopic best-response bidding strategy in any of the auction designs. Nevertheless, we achieved high efficiency levels in all auction designs. Furthermore, we identified significant differences in the auctioneer revenue depending on the auction design, but not on the number of the auc- tioned items (3, 6, and 9). We also observed a very low speed of convergence of the ICA design with non-linear personalized prices, which makes it (at least in its current form without using proxy agents) hardly suitable for practical applications. Zusammenfassung Auktionen haben in den letzten Jahren zunehmende Aufmerksamkeit in In- formatik und Wirtschaftswissenschaften gewonnen, da sie zur effizienten Al- lokation von Ressourcen eingesetzt werden k¨onnen. Zu ihren gr¨oßten Ein- satzgebieten geh¨oren unter anderem die Finanzbranche und E-Commerce. In vielen F¨allenwurden dabei neue Auktionsmechanismen nachgefragt, die kom- plexe Gebote auf mehrere G¨uteroder unterschiedliche Eigenschaften eines Gutes erm¨oglichen. Abgesehen von der strategischen Komplexit¨at,wird die Konstruktion solcher Verfahren zus¨atzlich durch die Komplexit¨at der dort auftretenden Berechnungsprobleme erschwert. Zum Beispiel geh¨ortdas Al- lokationsproblem bei kombinatorischen Auktionen zur Klasse der NP-schweren Probleme. In j¨ungster Zeit haben sich Wissenschaftler vorwiegend auf der Preissetzung und auf den Arten der als Feedback ¨ubermittelten Informationen fokussiert. Iterative kombinatorische Auktionen (ICAs) sind IT-basierte ¨okonomische Mechanismen, in denen Bieter die M¨oglichkeit haben, Gebote auf untrennbare G¨uterb¨undelin mehreren Runden iterativ abzugeben. Nach jeder Runde erhal- ten die Bieter vom Auktionator Informationen zu aktuellen Preisen und/oder der aktuellen Zwischenallokation. In der Literatur wurden mehrere Auk- tionsverfahren vorgeschlagen, aber ihr Verhalten unter unterschiedlichen Rah- menbedingungen wurde zu wenig untersucht. Wegen ihrer diskreter Struk- tur und komplexer Bietregeln, wird die spieltheoretische Analyse von ICAs iii iv wesentlich erschwert. In der Literatur findet man lediglich Equilibrium- Analysen von ICAs mit nichtlinearen personalisierten Preisen unter sehr stren- gen Annahmen ¨uber die verfolgten Bietstrategien. Im Gegenteil, ICAs mit linearen anonymen Preisen wurden erfolgreich in Feldstudien und im Labor eingesetzt. Rechensimulationen und Laborexperimente k¨onnenbei der Analyse und Ver- gleich von Auktionsformaten und bei der Untersuchung der Auswirkungen von unterschiedlichen Konfigurationsparametern eine große Hilfe leisten. In unseren Forschungsprojekten wollten wir diverse existierende Auktionsmech- anismen vergleichen und neue, verbesserte, Auktionsregeln entwickeln. Dabei haben wir uns auf Auktionen mit linearen anonymen Preisen konzentriert, aber auch ein Auktionsformat mit nicht-linearen personalisierten Preisen un- tersucht. In den Rechensimulationen haben wir drei ausgew¨ahlteICA Formate mit lin- earen anonymen Preisen und die VCG-Auktion verglichen, indem die alloka- tive Effizienz, die Gewinnverteilung und die Konvergenzgeschwindigkeit unter Annahmen von unterschiedlichen Wertemodellen und Bietstrategien gemessen wurden. Dabei haben die untersuchten ICAs mit linearen Preisen bei unter- schiedlichen Wertemodellen und sogar mit hohen Synergien zwischen einzelnen G¨uternsehr gute Ergebnisse geliefert. Wir haben allerdings signifikante Un- terschiede in der Effizienz und Gewinnverteilung zwischen den einzelnen Auk- tionsformaten festgestellt. Auch bei heuristischen Bietstrategien, bei denen die Bietagente nur auf eine zuf¨allig ausgew¨ahlte Untermenge der momentan besten B¨undel Gebote abgeben, haben wir hohe Effizienzgrade beobachtet. Wir haben auch mehrere neue Preisberechnungs-, Aktivit¨ats- und Abschlussregeln en- twickelt, mit denen die Auktionsergebnisse deutlich verbessert werden kon- nten. In den Laborexperimenten haben wir dieselben Auktionsformate und ein ICA mit nicht-linearen personalisierten Preisen im Bezug auf dieselben Kriterien v verglichen. Wir haben viele ¨ahnliche Ph¨anomena wie bei unseren Simula- tionsergebnissen identifiziert, aber auch ein sehr heterogenes Bietverhalten beobachtet, wobei bei keinem der Auktionsformate eine Analogie zur “my- opic best-response” Strategie ersichtlich war. Nichtsdestotrotz haben wir bei allen Auktionsformaten hohe Effizienzgrade erzielt. Außerdem haben wir sig- nifikante Unterschiede in der Gewinnverteilung beobachtet, die vom Auktions- format, aber nicht von der G¨uterzahl(3, 9 und 9) beeinflusst wurden. Beim untersuchten ICA mit nicht-linearen personalisierten Preisen war die Konver- genzgeschwindigkeit sehr niedrig, was dieses Auktionsformat (zumindest in der aktuellen Form ohne Proxy-Agenten) f¨urpraktische Anwendungen kaum brauchbar macht. vi Acknowledgments This dissertation is a result of many years of work and several important decisions and events, some carefully planned, and others happened purely by chance. On this way, I received help and support from many people, who directly or indirectly contributed to this work. Above all, I would like to thank my adviser Prof. Dr. Martin Bichler for giving me the chance to do my doctoral research at his Chair of Internet-based Information Systems at the TU M¨unchen. He was not only always available when I needed his help and input, but also helped in finding a highly interesting research direction and constantly encouraged and guided me through the ups and downs during my work. I could not have imagined a better adviser and mentor for my thesis than him. A special thanks is also addressed to all who worked in our research project. With my college Pasha Shabalin we were able to extend our research area considerably. The results presented in this dissertation would also not be pos- sible without help of our former students, who invested much time, creativity, and effort into our project. In particular,
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