6533b7d2fe1ef96bd125eb3e

RESEARCH PRODUCT

NASH EQUILIBRIA IN A MODEL OF MULTIPRODUCT PRICE COMPETITION: AN ASSIGNMENT PROBLEM

Amparo UrbanoIván Arribas

subject

TheoryofComputation_MISCELLANEOUSEconomics and EconometricsComputer Science::Computer Science and Game TheoryApplied Mathematicsjel:D41jel:D72TheoryofComputation_GENERALCooperative game theoryjel:D21jel:D43Extensive-form gameSubgame perfect equilibriumCompetition (economics)Microeconomicssymbols.namesakeMarkov perfect equilibriumSubgameNash equilibriumMultiproduct price competition interger programming subgame perfect nash equilibriaStackelberg competitionEconomicssymbolsMathematical economics

description

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.

yearjournalcountryeditionlanguage
2003-06-01
http://www.ivie.es/downloads/docs/wpasad/wpasad-2003-21.pdf