We consider such a problem: Multiple sellers sell a family of
substitutable perishable products in a common market with
correlative random demands. Due to the perishable nature of a
product, delivery time directly affects its freshness level, which
in turn affects its demand. Each seller's demand is formulated as
a function of all sellers' prices and delivery-times. To maximize
his own expected profit, each seller needs to set his selling
price and delivery time simultaneously, by taking into account his
competitors' reactions. We present three models to address
different practical situations. In Model I, we assume that each
seller faces constant operating and purchasing costs, but is subject to
a given service reliability constraint. In contrast, we assume
delivery-time dependent operating and purchasing costs without
service reliability constraints in Model II and Model III
respectively. We establish the existence of a price and
delivery-time equilibrium, under mild conditions in Model I and II,
and restrictive conditions in Model III. A novel method is adopted
to establish the uniqueness of the equilibrium in Model I, and an
iterative procedure is designed to compute the equilibrium prices
and delivery-times in Model III.
Mathematics Subject Classification:
Primary: 91A10, 91A4.
Xiaolin Xu, Xiaoqiang Cai. Price and delivery-time competition of perishable products: Existence and uniqueness of Nash equilibrium. Journal of Industrial & Management Optimization,
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