Theory of Computing Systems

, Volume 59, Issue 1, pp 1–23 | Cite as

On the Stability of Generalized Second Price Auctions with Budgets

  • Josep Díaz
  • Ioannis Giotis
  • Lefteris Kirousis
  • Evangelos Markakis
  • Maria Serna


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.


Auctions Second price Sponsored search Keyword auctions 



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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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Josep Díaz
    • 1
  • Ioannis Giotis
    • 1
  • Lefteris Kirousis
    • 2
    • 3
  • Evangelos Markakis
    • 4
  • Maria Serna
    • 1
  1. 1.Departament de Llenguatges i Sistemes InformaticsUniversitat Politecnica de CatalunyaBarcelonaSpain
  2. 2.Department of MathematicsNational and Kapodistrian University of AthensAthensGreece
  3. 3.Computer Technology Institute and Press “Diophantus”AthensGreece
  4. 4.Department of InformaticsAthens University of Economics and BusinessAthensGreece

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