Price Competition Based on Relative Prices

56 Pages Posted: 28 Feb 2013 Last revised: 15 Sep 2016

See all articles by Awi Federgruen

Awi Federgruen

Columbia Business School - Decision Risk and Operations

Lijian Lu

Columbia University - Columbia Business School

Date Written: February 16, 2016


We consider price competition models for oligopolistic markets, in which the consumer reacts to relative rather than absolute prices, where the relative price is defined as the difference between the absolute price and a given reference value. Such settings arise, for example, when the full retail price earned by the 'retailer' is reduced by virtue of a third party offering a subsidy or a rebate or in prospect theoretical models in which customers establish a reference price and base their choices on the differentials with respect to the reference price. When choosing among the various competing options, the consumer trades off the net price paid with various other product or service attributes, as in standard price competition models. The reference price may be exogenously specified and pre-announced to the competing firms. Alternatively, it may be endogenously determined, as a function of the set of absolute prices selected by the competing firms, for example the lowest or the second lowest price.

We review five different application areas where the above model structure arises. We then characterize the equilibrium behavior under a general reference value scheme of the above type; this in a base model, where we assume that the consumer choice model is of the general MultiNomialLogit (MNL) type. We also derive comparison results for the price equilibria that arise under alternative subsidy schemes. These comparisons have important implications for the design of subsidy schemes.

Suggested Citation

Federgruen, Awi and Lu, Lijian, Price Competition Based on Relative Prices (February 16, 2016). Columbia Business School Research Paper No. 13-9. Available at SSRN: or

Awi Federgruen

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Lijian Lu (Contact Author)

Columbia University - Columbia Business School ( email )

3022 Broadway
New York, NY 10027
United States

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