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

  • Arribas, Ivan
  • Urbano, Amparo

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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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 41 (2005)
Issue (Month): 3 (April)
Pages: 351-385

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Handle: RePEc:eee:mateco:v:41:y:2005:i:3:p:351-385
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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