Advertising Equilibrium under Each Channel Structure

We first derive the advertising equilibrium under each channel structure. To this end, we must solve the game backwards by first characterizing the equilibrium pricing strategies for a given profile of advertising strategies. The nature of the pricing game and the specific timing

1This assumption is made merely for expositional convenience; it implies that the initial sizes of the manufacturers’ local markets and the common market are the same.

of making these decisions critically depend on the channel structure, which we describe in detail below.

In the integrated channel, manufacturer i’s profit can be written as:

Π^I_i = max

pi

piqi, i= 1, 2,

where the superscript I stands for “integrated” and the demand qi has been specified in (1).

In equilibrium, each manufacturer maximizes his own profit by selecting the price. In the delegated channel, we shall first start with the retailer’s problem of determining the optimal retail price pi:

πi = max

pi

{(pi− wi)qi}, i = 1, 2,

where wi denotes Mi’s posted wholesale price. Accordingly, a manufacturer then determines the optimal wholesale price by solving

Π^D_i = max

wi

wiqi, i= 1, 2,

where the superscript D stands for “delegated” and qi depends on the retailer’s pricing decision through (1). Finally, in the common retailer channel, given the manufacturers’

advertising strategies and the wholesale prices, the profit of the common retailer, denoted by πR, is:

πR = max

p₁,p₂ {(p1− w1)q1+ (p2− w2)q2}, and a manufacturer’s profit is:

Π^C_i = max

wi

wiqi, i= 1, 2,

where the superscript C indicates the “common retailer channel.”

With these objective functions, we can characterize the equilibrium pricing strategies for the manufacturers and the retailers. After these steps, we can then formulate conceptually the normal-form game of the manufacturers’ advertising competition in Table 1. In Table 1, Π^k_i(s, t) denotes the manufacturer i’s profit under channel structure k ∈ {I, D, C}. The two arguments s and t correspond to the manufacturer’s own advertising strategy and its rival’s advertising strategy, where “N” means no advertising, “I” means informative advertising,

Table 1: Manufacturers’ Advertising Game

M₂ N (No Ads) I (Informative Ads) P (Persuasive Ads) M1

N Π^k₁(N, N), Π^k₂(N, N) Π^k₁(N, I), Π^k₂(N, I) Π^k₁(N, P ), Π^k₂(N, P ) I Π^k₁(I, N), Π^k₂(I, N) Π^k₁(I, I), Π^k₂(I, I) Π^k₁(I, P ), Π^k₂(I, P ) P Π^k₁(P, N), Π^k₂(P, N) Π^k₁(P, I), Π^k₂(P, I) Π^k₁(P, P ), Π^k₂(P, P )

and “P ” means persuasive advertising. Detailed expressions of these profit functions are presented in the appendix.

Table 1 allows us to derive the equilibrium advertising strategies under each channel context. For ease of exposition, we demonstrate a generic illustration for the regions of equilibrium advertising strategy profile in Figure 1, where (I, I) is the dominant-strategy equilibria in Region 1, (P, P ) in Region 3, and an asymmetric equilibrium (I, P ) or (P, I) in between these zones (labeled as Region 2). Based on Figure 1, we can derive the equilibrium advertising strategies under each channel context that are summarized in Proposition 1:

Proposition 1.In all channel contexts, for any specific value of γ, there exist corresponding thresholds θ_a^k and θ_b^k (θ^k_b > θ^k_a, k= I, D, C) such that manufacturers engage in informative advertising whenever θ < θ^k_a but persuasive advertising whenever θ > θ_b^k. Moreover, both thresholds θ^k_a and θ^k_b decrease as persuasive advertising is more effective (γ decreases).

As shown in Figure 1, when the products are highly substitutable, both manufacturers find it optimal to engage in persuasive advertising. On the contrary, when the product differentiation is relatively significant, informative advertising emerges as an optimal strategy for the manufacturers. In the intermediate cases, manufacturers intend to differentiate in their advertising strategies to mitigate the competition.

To understand the results of Proposition 1, let us recall the strategic motives of the informative and persuasive advertising. As aforementioned in Section 2.2, informative ad-vertising is intended to inform consumers who originally are familiar with the rival product

Figure 1: Advertising Equilibrium in Different Channel Contexts.

(i.e., G1 or G2) the presence of the advertised product. Therefore, informative advertising enlarges the advertising manufacturer’s effective demand; this is referred to as the demand-expanding effect. At the same time, the invasion of the advertising manufacturer in the rival’s local market may trigger the rival’s counteraction and therefore may lead to more in-tense competition (referred to as the competition-enhancing effect). The demand-expanding effect works in favor of the advertising manufacturer, whereas the competition-enhancing effect may drive down his profit.

On the contrary, persuasive advertising affects the preferences of consumers in the com-mon pool (Gc). It reduce the product substitution between m1 and m2. This is referred to as competition-mitigating effect. At the same time, while using persuasive advertising, the manufacturer may attempt to induce a higher retail price in response to the enhanced product differentiation. This increased price in turn may make the consumers in the local market (group Gi) unwilling to purchase from the manufacturer. We label this force as the demand-shrinking effect. The competition-mitigating effect works in favor of the advertising manufacturer, whereas the demand-shrinking effect may drive down his profit.

The above descriptions allow us to relate these effects to the inherent degree of product differentiation, θ, and the effectiveness of persuasive advertising, γ. Since both the demand-expanding effect and the demand-shrinking effect focus on how a consumer (either in the common pool or in the local market) responds to the price change of a manufacturer’s own product, they are not affected by the specific values of θ and γ.² On the contrary, how strong the competition-enhancing and the competition-mitigating effects are crucially depends on these values. Specifically, when the products are close substitutes (θ is high), a manufacturer’s informative advertising is likely to induce the rival’s counteraction, thereby leading to a strong competition-enhancing effect. As γ becomes lower, persuasive advertising shifts the consumers’ preferences more effectively; thus, the competition-mitigating effect is stronger.

With these taxonomies in mind, we can now articulate the strategic roles of manufactur-ers’ advertising. From Figure 1, when persuasive advertising is highly ineffective (a higher γ) and the product are sufficiently differentiated (a lower θ), the competition-enhancing ef-fect is relatively insignificant and the competition-mitigating efef-fect does not generate a high profit gain for the advertising manufacturer. Consequently, it is more profitable to engage in informative advertising and (I, I) emerges as the equilibrium outcome. However, as the products become highly substitutable (a higher θ) and persuasive advertising is highly effec-tive (a lower γ), both the competition-enhancing effect and competition-mitigating effect will become active. This implies that informative advertising would trigger severe competition between the manufacturers; on the contrary, persuasive advertising allows the manufacturers to differentiate their markets more effectively. Consequently, persuasive advertising becomes a more favorable strategy and either (P, I) or (P, P ) occurs in equilibrium.

Having discussed the common features of the equilibrium outcomes, in the remainder of this section, we compare the equilibrium outcomes across the channel structures. This allows us to articulate the strategic roles of informative and persuasive advertising under different channel structures.

2However, these two effects are highly sensitive to β, as will be discussed in Section 2.3.3.