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Selling Complementary Goods: Dynamics, Efficiency and Revenue

Authors Moshe Babaioff, Liad Blumrosen, Noam Nisan

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Moshe Babaioff
Liad Blumrosen
Noam Nisan

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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) https://doi.org/10.4230/LIPIcs.ICALP.2017.134

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.

Subject Classification

Keywords
  • Complements
  • Pricing
  • Networks
  • Game Theory
  • Price of Stability

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