Pricing Under Dynamic Competition When Loyal Consumers Stockpile

Posted: 5 Apr 2015 Last revised: 2 Mar 2021

See all articles by Manish Gangwar

Manish Gangwar

Indian School of Business (ISB), Hyderabad

Nanda S. Kumar

University of Texas at Dallas - Department of Marketing

Ram C. Rao

The University of Texas at Dallas, Naveen Jindal School of Management

Date Written: October 27, 2015

Abstract

Increased sales due to promotions could be at the expense of competitors: such sales come from consumers with relatively weak brand preferences. However, increased sales from brand loyal consumers could well cannibalize sales of the promoted brand. An unintended consequence of promotions is that loyal consumers who otherwise would be willing to pay high prices may strategically stockpile at low prices to reduce their cost. What is its impact on firms’ profits? How should firms adapt their pricing to consumer stockpiling? To answer these questions we analyze an infinite horizon dynamic model of competition under duopoly and derive the Markov Perfect Equilibrium pricing strategies.

Contrary to intuition we find that strategic stockpiling by loyal consumers at low prices does not reduce firms’ long-run profits if (i) initial consumer inventory is zero and (ii) firms employ the Nash equilibrium strategies that maximize the present value of future profits. Managers’ perception of losses probably reflects the fact that they encounter situations in which consumers have stockpiled in the past. We then analytically derive an upper bound on the losses after consumer stockpiling and show that it is relatively small. We derive the mixed strategy equilibrium that serves as a guide for managers on how to adapt pricing strategies to meet the challenge of stockpiling by loyal consumers. A particularly novel aspect of these strategies is that firms’ equilibrium pricing distributions can have a mass point in the interior of the support. Further, when the equilibrium pricing is compared to the situation with no stockpiling, we find that firms move away from frequently promoting below the stockpiling threshold, and moreover the probability of charging the reservation price increases. Finally, a prediction of our model is a positive inter-temporal correlation in prices implying, somewhat counter-intuitively, that in equilibrium deep promotions are followed by deep promotions.

Keywords: Game Theory, Consumer Stockpiling, Promotional Strategies, Loyal Consumers, Interior Mass Point, Pricing Distribution, Pricing

JEL Classification: C72, C73, D43, M21, M31

Suggested Citation

Gangwar, Manish and Kumar, Nanda S. and Rao, Ram C., Pricing Under Dynamic Competition When Loyal Consumers Stockpile (October 27, 2015). Indian School of Business Research Paper Series, Available at SSRN: https://ssrn.com/abstract=2589695 or http://dx.doi.org/10.2139/ssrn.2589695

Manish Gangwar

Indian School of Business (ISB), Hyderabad ( email )

Hyderabad, Gachibowli 500111
India

HOME PAGE: http://https://www.isb.edu/en/research-thought-leadership/faculty/pages/manish-gangwar.html

Nanda S. Kumar

University of Texas at Dallas - Department of Marketing ( email )

Dallas, TX
United States
972-883 6426 (Phone)
972-883 2799/972-883 6727 (Fax)

HOME PAGE: http://www.utdallas.edu/~nkumar

Ram C. Rao (Contact Author)

The University of Texas at Dallas, Naveen Jindal School of Management ( email )

Dallas, TX
United States
972-883-2580 (Phone)
972-883-6727 (Fax)

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