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Price Competition with the Attraction Demand Model: Existence of Unique Equilibrium and Its Stability

Industrial Engineering and Operations Research Department, Columbia University, 500 West 120th Street, New York, New York 10027
Industrial Engineering and Operations Research Department, Columbia University, 500 West 120th Street, New York, New York 10027
Division of Applied Mathematics, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, South Korea
Nomis Solutions, Inc., 1111 Bayhill Drive, San Bruno, California 94066
gmg2{at}columbia.edu
th2113{at}columbia.edu
wanmokang{at}gmail.com
robert.phillips{at}nomissolutions.com

We show the existence of Nash equilibria in a Bertrand oligopoly price competition game using a possibly asymmetric attraction demand model with convex costs under mild assumptions. We show that the equilibrium is unique and globally stable. To our knowledge, this is the first paper to show the existence of a unique equilibrium with both nonlinear demand and nonlinear costs. In addition, we guarantee the linear convergence rate of tatônnement. We illustrate the applicability of this approach with several examples arising from operational considerations that are often ignored in the economics literature.

Key Words: price competition; oligopoly; attraction demand model; Nash equilibrium; convex costs
History: Received: June 28, 2004;

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