Dilution

Recall that the weight between nodesiandj is

wij =

P

p∈Ppipj |P|

The possible sources of brand dilution discussed in section 1.2.3 all involved pairing a brand identifier Bwith an incongruent product. Incongruence simply means that the original brand differs from the

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In a multi-period model where the the experience setPincludes consumption experiences as well as advertisements the connection strengths will reflect a mixture of informative experiences and advertisements.

x 1 x2

Indifference curves when neither firm advertises

0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 x 1 x2

Indifference curves when F1 advertises

0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10

Figure 1.5: Indifference curves when neither firm advertises (left), and when firm 1 advertises (right).

other product on one or more attributes. We can quantify dilution on this level easily by considering the marginal effect of an incongruous advertisement on the connection strength between the brand name and the differing attribute. Without loss of generality, assume that the original brand, B is always paired with some attribute Y. The new product advertising the brand nameB with either Y = 0 or Y = −1. Let P0

be the set of advertisements for the original brand, and let a be an advertisement for the new product. Assume that for all other patterns in the original experience set, p∈P,p6∈P0, the state of the brand node is 0

∆wBY = P p∈P]apBpY |P|+ 1 − P p∈PpBpY |P| = |P0 |+aBaY |P|+ 1 − |P0 | |P| Notice that this effect is larger when

1. aY =−1 instead of 0

2. The size ofP0 is small (when there hasn’t been as much advertising for the original brand)

The second implication is consistent with Morrin and Jacoby’s finding that trademark dilution is more pronounced for less familiar (read less advertised) brands. Since the size of the effect on the connection weight is inversely proportional to the number of advertisements for the original brand, products with fewer advertisements are more vulnerable to trademark dilution.

But brand image is not simply a brand’s association with one attribute, but an entire pattern of attributes. Dilution will occur for every attribute of the original product that differs from the new product. In addition, the association between the brand name and the attribute isn’t the only one being diluted, connections among the attributes themselves will also be diluted. Since multiple connections are diluted, the aggregate effect of the new ad on theinput to any given node is proportional to the number of characteristics where the two products differ. This, possibly large, decrease in input to the node may change the state of attributeY inVB_{, the perceived characteristics}

of the original product.

Assuming that the state ofY inVB goes from 1 to 0, the change in marginal utility of product

igiven some fixed endowment will be:

∆∂u

∂xi =−

γY

3 (xi+eY)

−2/3_<0

whereeY is the total amount of attributeY from the initial endowment andγY >0 is the attribute utility coefficient forY.

This decrease in marginal utility is possible for every diluted positive association and is cumu- lative. If several positive attributes, Y1, . . . , Yk are no longer active in VB the change in utility is ∆∂u ∂xi =− k X j=1 γYj 3 (xi+eYj)− 2/3

Since this decrease occurs at all levels of consumption, the consumer’s demand for product i is

decreasing in the number of diluted positive attributes.17

These implications are supported by the findings in marketing that trademark and brand dilution is worse when the products sharing the brand or trademark are more dissimilar.

Notice that connections strengths are only diluted for the changed attributes. The connections between any consistent set of attributes will be reinforced by ads for both the parent brand and the extension. This is consistent with Dacin and Smith’s finding that brands associated with a variety of products, but consistent on quality, are less vulnerable to dilution. Here, every advertisement for the brand reinforces connections between the brand identifiers and quality, so the dilution of the other connections is less relevant.

1.5.2

Spillover

In the context of this model, a spillover is simply the activation of a positive attribute due to

advertising for a different product. Every advertisement affects all _{of the network connections, so}

advertisements associating a particular brand and product with a social attributeY will strengthen

the relationship between the brand andY, but it will also strengthen the association between the

product category itself. This product category spillover is consistent with Seldon’s finding that cigarette advertisements positively affected the demand curve for the entire industry as well as the specific demand for the advertising brand.

Applying the model to brand extensions again, notice that the marginal effect of advertisements

for both the parent brand and the extensions is to increase _{the connection strength between the}

brand name and positive shared attributes. Using the same notation used in the section on dilution

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notice that the marginal effect of a single advertisement for the extension on the association between the brand and a positive social attributeY is once again

∆wBY = P p∈P]apBpY |P|+ 1 − P p∈PpBpY |P| = |P0 |+aBaY |P|+ 1 − |P0 | |P|

Only in this case aBaY = 1 so the effect is positive. Notice that once again, this effect is

decreasing in the size ofP0, predicting that the reciprocal spillover effect from the extension to the parent brand is decreasing in the size ofP0

. This finding is consistent with studies that show that reciprocal spillover is is stronger forless familiar brands. (56)

Using exactly the same math as above, we see that advertising that enforces the connection between the brand and a positive attribute will weakly increase the marginal utility of both the original and extended products at all consumption levels. In general, the model agrees with findings in the marketing literature that consistency between a brand and its extension will facilitate spillover effects in both directions.

The model also helps to explain spillover effects from trivial attributes when their irrelevance to the product is known. Supporting the model prediction that mere association is enough to affect evaluation is Gilovich’s finding that sportswriters’ evaluations of college football players are affected by irrelevant information such as the fact that the college player was from the same hometown as a famous NFL player. (24) Here, the trivial attribute (hometown) establishes an indirect association with the athletic success of the professional player, i.e., the association of the hometown with success spills over to college player.