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DOI: 10.4230/LIPIcs.ICALP.2017.134

Selling Complementary Goods: Dynamics, Efficiency and Revenue

Authors: Moshe Babaioff, Liad Blumrosen, and Noam Nisan

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract

We consider a price competition between two sellers of perfect-complement goods. Each seller posts a price for the good it sells, but the demand is determined according to the sum of prices. This is a classic model by Cournot (1838), who showed that in this setting a monopoly that sells both goods is better for the society than two competing sellers. We show that non-trivial pure Nash equilibria always exist in this game. We also quantify Cournot's observation with respect to both the optimal welfare and the monopoly revenue. We then prove a series of mostly negative results regarding the convergence of best response dynamics to equilibria in such games.

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Moshe Babaioff, Liad Blumrosen, and Noam Nisan. Selling Complementary Goods: Dynamics, Efficiency and Revenue. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 134:1-134:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{babaioff_et_al:LIPIcs.ICALP.2017.134,
  author =	{Babaioff, Moshe and Blumrosen, Liad and Nisan, Noam},
  title =	{{Selling Complementary Goods: Dynamics, Efficiency and Revenue}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{134:1--134:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.134},
  URN =		{urn:nbn:de:0030-drops-74757},
  doi =		{10.4230/LIPIcs.ICALP.2017.134},
  annote =	{Keywords: Complements, Pricing, Networks, Game Theory, Price of Stability}
}

Document

DOI: 10.4230/LIPIcs.ICALP.2016.140

Networks of Complements

Authors: Moshe Babaioff, Liad Blumrosen, and Noam Nisan

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract

We consider a network of sellers, each selling a single product, where the graph structure represents pair-wise complementarities between products. We study how the network structure affects revenue and social welfare of equilibria of the pricing game between the sellers. We prove positive and negative results, both of "Price of Anarchy" and of "Price of Stability" type, for special families of graphs (paths, cycles) as well as more general ones (trees, graphs). We describe best-reply dynamics that converge to non-trivial equilibrium in several families of graphs, and we use these dynamics to prove the existence of approximately-efficient equilibria.

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Moshe Babaioff, Liad Blumrosen, and Noam Nisan. Networks of Complements. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 140:1-140:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{babaioff_et_al:LIPIcs.ICALP.2016.140,
  author =	{Babaioff, Moshe and Blumrosen, Liad and Nisan, Noam},
  title =	{{Networks of Complements}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{140:1--140:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.140},
  URN =		{urn:nbn:de:0030-drops-62849},
  doi =		{10.4230/LIPIcs.ICALP.2016.140},
  annote =	{Keywords: Complements, Pricing, Networks, Game Theory, Price of Stability}
}

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Selling Complementary Goods: Dynamics, Efficiency and Revenue

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Networks of Complements

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