We characterize the equilibrium behavior in a broad class of competition models in which the competing firms' market shares are given by an attraction model, and the aggregate sales in the industry depend on the aggregate attraction value according to a general function. Each firm's revenues and costs are proportional with its expected sales volume, with a cost rate that depends on the firm's chosen attraction value according to an arbitrary increasing function. Whereas most existing competition papers with attraction models can be viewed as special cases of this general model, we apply our general results to a new set of quality competition models. Here an industry has N suppliers of a given product, who compete for the business of one or more buyers. Each of the suppliers encounters an uncertain yield factor, with a given general yield distribution. The buyers face uncertain demands over the course of a given sales season. The suppliers compete by selecting key characteristics of their yield distributions, either their means, their standard deviations, or both. These choices have implications for their per-unit cost rates.
Federgruen, Awi, and Nan Yang. "Competition under generalized attraction models: Applications to quality competition under yield uncertainty." Management Science 55, no. 12 (December 2009): 2028-2043.
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