Operations, Information and Decisions Papers

Document Type

Journal Article

Date of this Version

7-2010

Publication Source

Operations Research

Volume

58

Issue

4

Start Page

1133

Last Page

1147

DOI

10.1287/opre.1090.0797

Abstract

We study a dynamic pricing problem for a class of products with stable consumption patterns (e.g., household items, staple foods). Consumers may stock up the product at current prices for future consumption, but they incur inventory holding costs. We model this situation as a dynamic game over an infinite time horizon: in each period, the seller sets a price, and each consumer chooses how many units to buy. We develop a solution methodology based on rational expectations. By endowing each player with beliefs, we decouple the dynamic game into individual dynamic programs for each player. We solve for the rational expectations equilibrium, where all players make optimal dynamic decisions given correct beliefs about others' behavior. In equilibrium, the seller may either charge a constant fixed price or offer periodic price promotions at predictable time intervals. We show that promotions are useful when frequent shoppers are willing to pay more for the product than are occasional shoppers. We also develop several model extensions to study the impact of consumer stockpiling on the seller's inventory, production, and rationing strategies.

Keywords

dynamic pricing, stockpiling, consumer inventory, promotions, rational expectations, price discrimination

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Date Posted: 27 November 2017

This document has been peer reviewed.