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On the Stability of Generalized Second Price Auctions with Budgets

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Abstract

The Generalized Second Price (GSP) auction used typically to model sponsored search auctions does not include the notion of budget constraints, which is present in practice. Motivated by this, we introduce the different variants of GSP auctions that take budgets into account in natural ways. We examine their stability by focusing on the existence of Nash equilibria and envy-free assignments. We highlight the differences between these mechanisms and find that only some of them exhibit both notions of stability. This shows the importance of carefully picking the right mechanism to ensure stable outcomes in the presence of budgets.

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Notes

  1. This assumption is derived from the distinct space these slots occupy on a web-page.

  2. In more detail, the instability arises when some player can alter his bid to raise someone else’ s price, forcing the mechanism to evict him from his slot based on budget constraints and subsequently benefiting the first player.

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Acknowledgements

We would like to thank Konstantinos Gavriil for pointing out to us the counterexample of Fig. 2, that without distinct budgets, envy-free assignments may fail to exist. We also want to thank Giorgos Birbas for valuable discussions during the preparation of this work.

This research has also been co-financed by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) - Research Funding Program: Thales. Investing in knowledge society through the European Social Fund.

Josep Díaz, Maria J. Serna and Ioannis Giotis supported by the CICYT project TIN-2007-66523 (FORMALISM).

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Authors and Affiliations

  1. Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Barcelona, Spain

    Josep Díaz, Ioannis Giotis & Maria Serna

  2. Department of Mathematics, National and Kapodistrian University of Athens, Athens, Greece

    Lefteris Kirousis

  3. Computer Technology Institute and Press “Diophantus”, Athens, Greece

    Lefteris Kirousis

  4. Department of Informatics, Athens University of Economics and Business, Athens, Greece

    Evangelos Markakis

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  1. Josep Díaz
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  2. Ioannis Giotis
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  5. Maria Serna
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Correspondence to Ioannis Giotis.

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Díaz, J., Giotis, I., Kirousis, L. et al. On the Stability of Generalized Second Price Auctions with Budgets. Theory Comput Syst 59, 1–23 (2016). https://doi.org/10.1007/s00224-015-9634-4

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