Generic and Brand Advertising Strategies Under Inter-Industry Competition

Abstract

Industries invest in over billion dollars annually to drive up the primary demand and to fence off competing new industries’ threat to their customer bases. Companies in addition to contributing to industry generic campaign also heavily rely on brand advertising in order to capture a greater market share. Using a game-theoretic approach, we study generic and brand advertising competition under such an inter-industry competitive framework. We built an analytical model to study two competing industries each simultaneously making generic advertising decisions followed by firms within each industry simultaneously conducting brand advertising. We found that the mere presence of a rival industry can act as an impetus for an industry to invest in generic advertising. Model analyses and numerical studies suggest that there is a clear interactive nature between the two types of advertising decisions under inter-industry competitive framework. The generic advertising spending of an industry increases as the firms within that industry are more asymmetric. While a firm’s brand advertising spending increases as the generic advertising of its associated industry becomes more effective and that of the rival industry becomes less effective. Extensions of the main model suggest that there is a first-mover advantage in generic advertising under inter-industry competition.

Appendix

1.1 Proof of Proposition 1

Based on the model setup in Section 3, profit function for firm i of industry j can be written as:

$$ {\pi}_{ij}=\left(\frac{M_{oj}+{\alpha}_j{G}_j}{M_{0 j}+{\alpha}_j{G}_j+{M}_{0,3- j}+{\alpha}_{3- j}{G}_{3- j}}\right)\left(\frac{\theta_{ij}{B}_{ij}^{1/2}}{\theta_{ij}{B}_{ij}^{1/2}+{\theta}_{3- i, j}{B}_{3- i, j}^{1/2}}\right){S}_j-{G}_{ij}-{B}_{ij},\mathrm{with}\; i, j=1,2. $$

(6)

Equilibrium brand advertising levels at the second stage of the game are obtained from simultaneously solving the first-order conditions $\frac{\partial {\pi}_{ij}}{\partial {B}_{ij}}=0$ and check the negative semi-definiteness of the second-order Hessian matrix, which results in

$$ {B}_{ij}=\frac{\theta_{ij}{\theta}_{3- i, j}{M}_j{s}_j}{2{\left({\theta}_{ij}+{\theta}_{3- i, j}\right)}^2} $$

(7)

Substitute M ₀₁ = ϕ, M ₀₂ = kϕ and (7) back to (6), sum over the profit functions of the two firms within each industry yields the industry total profit function:

$$ {\pi}_1=\left(\frac{\phi +{\alpha}_1{G}_1}{\phi +{\alpha}_1{G}_1+ k\phi +{\alpha}_2{G}_2}\right){Y}_1{s}_1-{G}_1;{\pi}_2=\left(\frac{k\phi +{\alpha}_2{G}_2}{\phi +{\alpha}_1{G}_1+ k\phi +{\alpha}_2{G}_2}\right){Y}_2{s}_2-{G}_2 $$

(8)

where ${Y}_j=1-\frac{\theta_{ij}{\theta}_{3- i, j}}{{\left({\theta}_{ij}+{\theta}_{3- i, j}\right)}^2}$, ∀i , j = 1 , 2.

Solving for $\frac{\partial {\pi}_j}{\partial {G}_j}=0$ and check the negative semi-definiteness of the second-order Hessian matrix yields the expressions of ${G}_j^{\ast }$ as in part 1 of Proposition 1. ${G}_j^{\ast }>0$ as long as $0<\phi <\frac{\lambda_1^2{\lambda}_2}{{\left({\lambda}_1+{\lambda}_2\right)}^2}$ (condition i) with λ _j  = α _j Y _j s _j  , j = 1 , 2.

We next check if an industry would still have incentive to invest positive amount for generic campaign when its rival industry does not conduct any generic advertising. Suppose G ₂ = 0, straight profit maximization yields the optimal generic advertising level for industry 1 as:

$$ {G}_1^{\prime }=\frac{\sqrt{k{\phi \alpha}_1{Y}_1{s}_1}-\left(1+ k\right)\phi}{\alpha_1} $$

(9)

and the above (9) is positive as long as $0<\phi <\frac{k{\alpha}_1{Y}_1{s}_1}{{\left(1+ k\right)}^2}$ (condition ii). Similarly, we can derive the condition for ${G}_2^{\prime }>0$ if G ₁ = 0.

Combing conditions (i) and (ii) results in the parameter condition for part 1 of Proposition 1. Substituting ${G}_j^{\ast }$ back to (7) yields the equilibrium brand advertising levels reported in part 1 of Proposition 1. Finally, the feasibility conditions are satisfied by substituting the equilibrium generic-brand advertising levels back to the industry profit functions and found that ${\pi}_j^{\ast}\left({G}_j^{\ast },{B}_{ij}^{\ast}\right)>0$. Derivation of brand advertising levels for part 2 of Proposition 1 follows by substituting ${G}_j^{\ast }=0$ into (7) for profit maximization with respect to B _ij . This completes the proof. ■

1.2 Proof of Corollary 2

Taking partial derivatives of the equilibrium brand advertising level (${B}_{ij}^{\ast }$) in part 1 of Proposition 1 with respect to α _j and α _3 − j , Corollary 2 follows after straight algebraic arrangement. ■

1.3 Proof of Corollary 3

Taking partial derivatives of the equilibrium generic advertising level (${G}_j^{\ast }$) in Proposition 1 with respect to θ _ij and θ _{3 − i , j} , Corollary 3 follows as the product of these two partial derivatives is negative. ■

1.4 Proof of Proposition 2

The brand advertising decision at the last stage can be derived similarly as in proposition 1. Back to the second stage of the sequential game in Extension (Section 4.4) where industry 2 determines G ₂ given G ₁ and knowing how the firms across industries decide their brand advertising at the last stage. Profit maximization of π ₂ in (8) with respect to G ₂ yields

$$ {G}_2=\frac{\sqrt{\alpha_2{Y}_2{s}_2\left(\phi +{\alpha}_1{G}_1\right)}-{\alpha}_1{G}_1-\left(1+ k\right)\phi}{\alpha_2} $$

(10)

Finally, move back to the first stage where industry 1 decides G ₁ knowing how industry 2 would choose G ₂ and the consequent brand advertising decision at the firm level. Substitute G ₂ from (10) into π ₁ in (8), profit maximization with respect to yields

$$ {G}_1^{\ast \ast }=\frac{\lambda_1^2}{4{\alpha}_1{\lambda}_2}-\frac{\phi}{\alpha_1} $$

(11)

Substitute (11) back to (10) yields

$$ {G}_2^{\ast \ast }=\frac{\lambda_1\left(2{\lambda}_2-{\lambda}_1\right)}{4{\alpha}_2{\lambda}_2}-\frac{k\phi}{\alpha_2} $$

(12)

It can be shown by comparing (11), (12) with $\left({G}_1^{\ast },{G}_2^{\ast}\right)$ from Proposition 1 that ${G}_2^{\ast \ast }-{G}_2^{\ast }<0$, while ${G}_1^{\ast \ast }-{G}_1^{\ast }>0$ as long as ${\alpha}_1>\frac{\alpha_2{Y}_2{s}_2}{Y_1{S}_1}$. This completes the proof. ■