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 InfoPaper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2003-21.
Length: 48 pages
Date of creation: Jun 2003
Date of revision:
Publication status: Published by Ivie
Multiproduct price competition; interger programming; subgame perfect nash equilibria;
Other versions of this item:
- 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.
- 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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