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Computational Aspects of Multimarket Price Wars

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Internet and Network Economics (WINE 2009)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 5929))

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Abstract

We consider the complexity of decision making with regards to predatory pricing in multimarket oligopoly models. Specifically, we present multimarket extensions of the classical single-market models of Bertrand, Cournot and Stackelberg, and introduce the War Chest Minimization Problem. This is the natural problem of deciding whether a firm has a sufficiently large war chest to win a price war. On the negative side we show that, even with complete information, it is hard to obtain any multiplicative approximation guarantee for this problem. Moreover, these hardness results hold even in the simple case of linear demand, price, and cost functions. On the other hand, we give algorithms with arbitrarily small additive approximation guarantees for the Bertrand and Stackelberg multimarket models with linear demand, price, and cost functions. Furthermore, in the absence of fixed costs, this problem is solvable in polynomial time in all our models.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University,  

    Nithum Thain

  2. Department of Mathematics and Statistics and School of Computer Science, McGill University,  

    Adrian Vetta

Authors
  1. Nithum Thain
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  2. Adrian Vetta
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Editor information

Editors and Affiliations

  1. Department of Information and Systems, Sapienza University of Rome, Via Ariosto 25, 00185, Roma, Italy

    Stefano Leonardi

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Thain, N., Vetta, A. (2009). Computational Aspects of Multimarket Price Wars. In: Leonardi, S. (eds) Internet and Network Economics. WINE 2009. Lecture Notes in Computer Science, vol 5929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10841-9_28

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  • DOI: https://doi.org/10.1007/978-3-642-10841-9_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10840-2

  • Online ISBN: 978-3-642-10841-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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