Technical Note—Global Robust Stability in a General Price and Assortment Competition Model

Awi Federgruen () and Ming Hu ()
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Awi Federgruen: Graduate School of Business, Columbia University, New York, New York 10027
Ming Hu: Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada

Operations Research, 2021, vol. 69, issue 1, 164-174

Abstract: We analyze a general but parsimonious price competition model for an oligopoly in which each firm offers any number of products. The demand volumes are general piecewise affine functions of the full price vector, generated as the “regular” extension of a base set of affine functions. The model specifies a product assortment , along with their prices and demand volumes, in contrast to most commonly used demand models, such as the multinomial logit model or any of its variants. We show that a special equilibrium in this model has global robust stability . This means that, from any starting point, the market converges to this equilibrium when firms use a particular response mapping to dynamically adjust their own prices in response to their competitors’ prices. The mapping involves each firm optimizing its own prices over a limited subset of possible prices and requires each firm to only know the demand function and cost structure for its own products (but not for other firms’ products).

Keywords: equilibrium; price competition; assortment competition; robust global stability; best response; contraction mapping (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:69:y:2021:i:1:p:164-174

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