Recommendations to Facilitate Segmentation

From Propositions 2.1 and 2.2 partial segmenting equilibria exist only when the slope of the quality contingent price schedule is significantly high or low, respectively. The required big 𝑑𝑑(1 + 𝑟𝑟) (𝑚𝑚 + 1)⁄ value necessary to support the equilibrium in Proposition 2.1 and the small 𝑑𝑑(1 + 𝑟𝑟) (𝑚𝑚 + 1)⁄ value necessary to support the equilibrium in Proposition 2.2 are needed to ensure either very high or very low rewards to quality. In Proposition 2.3 we state that under moderate rewards to quality, segmentation of this type cannot exist.

Proposition 2.3.

For intermediate values of the discounted slope of the market price schedule ^{𝑑𝑑(1+𝑟𝑟)}

𝑚𝑚+1 in the interval �𝐸𝐸𝐿𝐿_{(𝐻𝐻>𝐿𝐿)}, 𝐿𝐿𝐿𝐿_{(𝐻𝐻<𝐿𝐿)}� partial segmenting equilibria do not exist.

An inspection of the bounds imposed on 𝑑𝑑(1 + 𝑟𝑟) (𝑚𝑚 + 1)⁄ in (2.24) and (2.29) yields that 𝐸𝐸𝐿𝐿_{(𝐻𝐻>𝐿𝐿)} < 𝐿𝐿𝐿𝐿_{(𝐻𝐻<𝐿𝐿)} implying that there is a nonempty interval of 𝑑𝑑(1 + 𝑟𝑟) (𝑚𝑚 + 1)⁄ values that cannot support this type of segmentation. (See Figure 2.4 for a visual representation of

Proposition 2.3.) The size of the interval of nonexistence is smaller as 𝛽𝛽 increases or as 𝑐𝑐 declines. Hence, when a bigger share of the population of consumers consists of information seekers and when the probability of finding a suitable vendor decreases (𝑐𝑐 declines), it is more likely that a partial segmenting equilibrium can arise (either in the form of 𝑅𝑅_𝐻𝐻< 𝑅𝑅_𝐿𝐿 or 𝑅𝑅_𝐻𝐻 >

𝑅𝑅𝐿𝐿).

Of the three types of equilibria we have considered it seems like the one characterized in Proposition 2.2 is the most likely to arise. The full segmenting equilibrium with both information seekers and one time shoppers being segmented requires unrealistically low values of the

parameter 𝑐𝑐. Such low values imply that consumers have to frequently sample vendors in the same category from a given platform before being able to find a suitable vendor, and that

platforms are forced to charge very low prices, as a result. In particular, when 𝑐𝑐 approaches zero, 𝑅𝑅_𝐻𝐻 = 𝑅𝑅𝐿𝐿= 0 in (2.19), (2.22), and (2.26). The partial segmenting equilibrium with 𝑅𝑅𝐻𝐻 < 𝑅𝑅𝐿𝐿 is

Partial Segmenting Equilibrium with 𝑅𝑅𝐻𝐻 > 𝑅𝑅_𝐿𝐿

Partial Segmenting Equilibrium with 𝑅𝑅𝐻𝐻 < 𝑅𝑅_𝐿𝐿 No Segmenting

Equilibrium

𝐸𝐸𝐿𝐿_{(𝐻𝐻>𝐿𝐿)} 𝐿𝐿𝐿𝐿_{(𝐻𝐻<𝐿𝐿)}

𝐿𝐿𝐿𝐿_{(𝐻𝐻>𝐿𝐿)} 𝐸𝐸𝐿𝐿_{(𝐻𝐻<𝐿𝐿)}

Figure 2.4 – Values of ^{𝐝𝐝(𝟏𝟏+𝐫𝐫)}

𝐦𝐦+𝟏𝟏 Supporting Partial Segmenting Equilibria

quality schedule, so much so, that the required steepness may even exceed the highest

willingness to pay for quality among consumers. Because markets where prices exceed consumer willingness to pay normally collapse, this type of segmentation is unlikely as well.

Sustaining the partial segmenting equilibrium with 𝑅𝑅𝐻𝐻 > 𝑅𝑅𝐿𝐿 requires more reasonable values of the parameters. The portion of the population that consists of information seekers should be sizable, yet not too large, and the required steepness of the quality-price schedule should be relatively small in comparison to the willingness to pay for higher quality in the consumer population. Viable markets normally have this latter characteristic. In the context of our model, a relatively flat quality price schedule arises in markets where offering higher quality is not extremely more costly for vendors than offering low quality (i.e., 𝑑𝑑 is small) and

consumers can easily detect and disseminate information about vendors who choose to lower quality below their established reputation (i.e., small 𝑟𝑟). Consumers can easily detect and disseminate quality information in categories where purchases are frequent and where quality is experience based as opposed to credence based (e.g., restaurants, fitness classes, and salon services vs. medical doctors and auto mechanics). Note that because the two platforms offer at the equilibrium deals at different prices, consumers and vendors can infer which platform represents, on average, higher quality vendors.

If segmentation fails, the platforms are not differentiated and the matching of consumers to vendors is completely random. With random matching, platforms compete fiercely on deal prices, and marginal cost pricing implies that 𝑅𝑅𝐻𝐻 = 𝑅𝑅𝐿𝐿 = 0. With segmentation, the platforms are vertically differentiated and they can charge positive deal prices. However, this vertical differentiation is not the result of platforms actually having control over the quality of the service they provide. Instead, the differentiation is the result of different segments of the vendor and

consumer populations choosing to interact with different platforms. In traditional models of vertical product differentiation, producers have full control over the qualities of the products they offer. In order to support segmentation they need to satisfy only one incentive compatibility constraint related to self-selection of the differentiated products by consumers. For

intermediaries that seek to match vendors with consumers there are, in fact, two separate incentive compatibility conditions that constrain the ability of the platforms to implement

segmentation. It is not only the choice of consumers but that of the vendors as well that has to be incorporated in ensuring the segmentation of each side of the market. The additional

self-selection constraint of the vendors makes it more difficult to implement equilibrium with vertically differentiated platforms. It is important, therefore, for the platforms to carefully select the categories of service that can support the partial segmentation characterized in Proposition 2.2.

It is noteworthy that the segmentation in our model is attained even though platforms have a single instrument at their disposal to generate differentiation: the price each of them charges for the deal. If additional instruments were available, we conjecture that the range of parameter values that could support segmentation would expand. One such instrument is a different sharing rule of the profits between the platform and the vendor (different values of 𝛼𝛼 selected by the platforms). In Appendix A we demonstrate, indeed, that it becomes easier for the platforms to implement segmentation when sharing rules are chosen strategically.