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Nash equilibria in a model of multiproduct price competition: an assignment problem

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  • Arribas, Ivan
  • Urbano, Amparo

Abstract

We study the market interaction of a finite number of single-product firms and a representative buyer, where the buyer consumes bundles of these goods. The buyers' value function determines their willingness to pay for subsets of goods. We show that subgame perfect Nash-equilibrium outcomes are solutions of the linear relaxation of an integer programming assignment problem and that they always exits. The (subgame perfect) Nash-equilibrium price set is characterized by the Pareto frontier of the associated dual problem's projection on the firms' price vectors. We identify the Nash-equilibrium prices for monotonic buyers' value functions and, more importantly, we show that some central solution concepts in cooperative game theory are (subgame perfect) equilibrium prices of our strategic game.
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  • Arribas, Ivan & Urbano, Amparo, 2005. "Nash equilibria in a model of multiproduct price competition: an assignment problem," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 351-385, April.
    • Handle: RePEc:eee:mateco:v:41:y:2005:i:3:p:351-385
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    1. Arribas, I. & Urbano, A., 2018. "Identification of efficient equilibria in multiproduct trading with indivisibilities and non-monotonicity," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 83-94.
    2. Arribas, I. & Urbano, A., 2017. "Multiproduct trading with a common agent under complete information: Existence and characterization of Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 167(C), pages 14-38.
    3. Ivan Arribas & Amparo Urbano, 2004. "Mixed Bundling Strategies And Multiproduct Price Competition," Working Papers. Serie AD 2004-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

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    More about this item

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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