Nash equilibria in a model of multiproduct price competition: an assignment problem
AbstractWe 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 41 (2005)
Issue (Month): 3 (April)
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Other versions of this item:
- Ivan Arribas & Amparo Urbano, 2003. "Nash Equilibria In A Model Of Multiproduct Price Competition: An Assignment Problem," Working Papers. Serie AD 2003-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- 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 and Pricing - - - Perfect Competition
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
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