Dynamic modeling of nontargeted and targeted advertising strategies in an oligopoly

Chloe A. Fletcher; Jason S. Howell

doi:10.3934/jdg.2017007

Article Contents

2017, Volume 4, Issue 2: 97-124. Doi: 10.3934/jdg.2017007

This issue Previous Article A simple family of solutions for forest games Next Article A continuous-time approach to online optimization

Dynamic modeling of nontargeted and targeted advertising strategies in an oligopoly

Chloe A. Fletcher and
Jason S. Howell^,

Department of Computer Science, College of Charleston, Charleston, SC 29424, USA

* Corresponding author: J. S. Howell
* Corresponding author: J. S. Howell

Received: April 30, 2016

Revised: November 30, 2016

Published: May 2017

Abstract Full Text(HTML) Figure(7) / Table(1) Related Papers Cited by

Abstract

With the growing collection of sales and marketing data and depth of detailed knowledge of consumer habits and trends, firms are gaining the capability to discern customers of other firms from the potential market of uncommitted consumers. Firms with this capability will be able to implement a strategy where the advertising effort towards customers of competing firms may differ from that towards uncommitted consumers. In this work, dynamic models for advertising in an oligopoly setting with fixed total market size and sales decay are presented. Two models are described in detail: a nontargeted model in which the advertising effort is the same for both categories of prospective customers, and a targeted model that gives firms the capability to allocate effort across the two categories differently. In the differential game setting, open-loop and closed-loop Nash equilibrium strategies are derived for both models. Several strategic questions that a firm may face when practicing targeted advertising on a fixed budget are discussed and addressed.

Keywords:

Mathematics Subject Classification: Primary: 91A23, 91A10; Secondary: 91A80, 90B60.

Citation:

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Figure 1. Solutions to (11)–(12) and closed-loop strategies (13)

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Figure 2. Solutions to (47)–(49) and closed-loop strategies (50)

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Figure 3. Values of $u_k^2$ from (82) that Maximize $\dot{s}_k$ for varying $\rho_k/\sigma_k$

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Figure 4. Dependence of $s_1$ on $c_1$ and $c_2$ in (85)

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Figure 5. Contour plot of $u_1^2$ that maximizes $s_1$ for $c_1$ and $c_2$ in (85)

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Figure 6. The solid curve indicates the value of $u_1^2$ that maximizes $s_1-s_2$, while the dotted curve represents the value of $u_1^2$ that maximizes $s_1$

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Figure 7. Value of $u_1$ that minimizes $\varepsilon$ in (92)

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Table 1. Summary of Related Works

	[11]	[8]	[9]	[33]	[12]	[18]	This work
Model Type	Duo.	Oligo.	Oligo.	Duo.	Duo.	Duo.	Oligo.
Sales Decay	No	No	No	Yes	No	No	Yes
Effort To Market Potential	Yes	Yes	Yes	Yes	No	Yes	Yes
Effort To Competitors' Customers	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Targeting	No	No	No	No	Yes	Yes	Yes
Time Horizon	Infinite	Infinite	Infinite	Finite	Infinite	Finite	Finite
Open-loop NE	Yes	Yes	Yes	Yes	Yes	No	Yes
Closed-loop NE	Yes	Yes	Yes	Yes	Yes	Yes	Yes

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