Digital platforms provide a variety of services that facilitate participation and business transactions by a variety of businesses, small and big. Among other things, some platforms enable help businesses expand their market reach through discovery of potential buyers. Some platforms provide support for fulfillment, covering delivery logistics, payment, and trust in transactions. Some platforms provide both categories of services.

This note will build a model to explore the business’s use of a marketplace platform to support discovery and/or fulfillment: whether, for each service, it should use the platform or not, and specifically the likelihood that the business will single-home with one platform vs multi-home and leverage both platforms. You will see that the answers will depend on

The degree of multi-homing on the customer side ($\frac{M}{M+2S}$ below).

The relative efficiency that the platform provides over the business’s do-it-yourself approach ($a$ relative too $\alpha$ for discovery, … and $t$ vs $\tau$ for fulfillment).

The (fixed) cost of joining the platform, hence cost of multi-homing, for the business.

The business’s efficiency in converting potential buyers to actual buyers ($p$).

1 Initial Setup

To make the analysis and exposition concrete, we assume that the actions follow the conversion funnel and flow depicted below. Specifically, we assume that (i) “discovery” reflects reaching a potential buyer, and (ii) a fraction $p$ of potential buyers so reached turn into actual sales. Also assume, without loss of generality, that each “customer” represents at most single-unit demand.

Consider a business that is considering employing a digital platform for one or both of two services, discovery and fulfillment. Let the total market size be denoted by $M + 2S$ (more on this choice of notation later). Suppose that in the absence of the platform, the business has an average per-sale customer discovery cost $\alpha$, per-unit fulfillment transaction cost $\tau$, besides a per-unit product cost $c$. Further, with the given level of market competition faced by the business, suppose that its revenue for $x$ sales is $\beta \sqrt{x}$, a function that captures diminishing marginal revenue per sale. Thus, $N$ customer discoveries result in a cost $\alpha N$, and lead to an expected fulfillment cost $p(\tau + c) N$ and revenue $\beta \sqrt{p N}$.

The firm seeks to maximize net profit $\Pi = \beta \sqrt{p N} - (\alpha + p(\tau + c)) N$. Setting the marginal revenue per discovery ($\frac{\beta \sqrt{p}}{2 \sqrt{N}}$) to equal the marginal cost implied by each discovery ($\alpha+p(\tau+c)$), the firm’s optimal operational outcomes (volume of customer discovery, sales, and profit) are as follows.
\[\begin{align} N^{\ast} &= p \left(\frac{\beta}{2(\alpha + p(\tau+ c))} \right) ^2 \tag{1.1} \\ Sales &= \left(\frac{\beta}{2(\frac{\alpha}{p} + (\tau+ c))} \right) ^2 \tag{1.2} \\ \Pi^{\ast} &= p \frac{\beta^2}{4(\alpha + p(\tau+ c))} \tag{1.3} \end{align}\]

so long as Sales ($=p \cdot N^{\ast}$) do not exceed $M + 2S$. For instance, if $M+2S =90$ (90 customers, see picture below) these equations yield an interior optimal solutionfor $\beta = 1000, 1100, 1200$ but the boundary solution takes over for the higher $\beta$.

2 Leveraging a Platform’s Discovery Services

Now suppose that there are two platforms that can assist the business in discovering customers, in other words providing access to monetization opportunities. Collectively, the platforms are able to address the market of $M + 2S$ customers. Of this, a segment $M$ frequents both platforms (multi-homes) while two separate segments of size $S$ each visit only platform 1 or 2 respectively.

Suppose the platform can help the business reach target market customers more efficiently than its traditional approaches for customer reach and discovery. This would imply, in the case of the two single-platform $S$ segments, that the platform offers a lower per-user acquisition cost $a < \alpha$ (in discovery costs, while the costs $\tau$ and $c$ remain unaffected). However, since some customers multi-home, some of each platform’s messaging will reach those customers twice. Hence, in expectation the conversion rate for such customers will be half that for $S$ type customers, due to the potentially double targeting, implying a per-unit discovery cost $2 a$. Combining these two groups, the average discovery cost per potential buyer is therefore $\left(\frac{M}{M+2S} + 1 \right) a$.

2.1 Multi-Homing for Discovery

If the business decides to multi-home over discovery platforms, then the counterpart of Eq. (1.1)-(1.3) is

\[\begin{align} N^{\ast} &= p \left(\frac{\beta}{2((\frac{M}{M+2S}+1)a + p(\tau+ c))} \right) ^2 \tag{2.1} \\ Sales &= \left(\frac{p \beta}{2((\frac{M}{M+2S}+1)a + p(\tau+ c))} \right) ^2 \tag{2.2}\\ \Pi^{\ast} &= p \frac{\beta^2}{4\left(\left(\frac{M}{M+2S} + 1 \right) a + p(\tau+ c) \right)} \tag{2.3} \end{align}\]

Trivially, this approach of multi-homing with both platforms is superior to going it alone if $\left(\frac{M}{M+2S} + 1 \right) a < \alpha$. Intuitively, this means that the better unit cost of discovery ($a < \alpha$) overcomes the inefficiency in discovery costs with $\frac{M}{M+2S}$ redundancy in discovery actions. This happens when the multi-homing segment (which creates inefficiency in discovery) is not too large, $M < \frac{2(\alpha-a)}{2a - \alpha} S$, or if the platforms are super-efficient at discovery, $\frac{a}{\alpha} < \frac{M+2S}{2M+2S}$. See the picture below for illustrative examples, with multiple panels (varying $a$ and $M$) and each panel showing the value $\frac{2(\alpha-a)}{2a - \alpha}$ for easy comparison with $M$.

2.2 Single-Homing for Discovery

If the business chooses to engage only one platform, and as before the platform offers a more efficient way to reach target customers at average per-unit discovery cost $a$, then the outcomes under this single-homing approach are

\[\begin{align} N^{\ast} &= p \left(\frac{\beta}{2(a + p(\tau+ c))} \right) ^2 \tag{2.4} \\ Sales &= \left(\frac{\beta}{2(\frac{a}{p} + (\tau+ c))} \right) ^2 \tag{2.5} \\ \Pi^{\ast} &= p \frac{\beta^2}{4(a + p(\tau+ c))} \tag{2.6} \end{align}\]

For the business, the downside of single-homing is that it would forfeit $S$ customers who are only on the other platform, thus reach a maximum of $S+M$ customers, implying a maximum of $p(S+M)$ sales. However, this reduced reach downside is irrelevant if the optimal sales under the do-it-yourself approach (Eq. (1.2)) were below $S+M$, and then the business would be better off single-homing vs self-managing discovery (and possibly even multi-homing). This condition corresponds to the condition that profit is decreasing at $N=S+M$ under the self-run discovery approach (i.e., $\pd{\Pi}{N} \vert_{N=S+M} < 0$), i.e., that $\frac{\beta}{2 \sqrt{p}\sqrt{S+M}} < (\alpha + p(\tau+c))$. Thus, the single-homing approach is more likely to work well when the multi-homing customer segment $M$ is large, or conversion rate $p$ is high (or $\alpha$ is large) because in these cases the business’s operations would not exceed the limited market reach it obtains under single-homing.

The converse possibility is that the single-homing profit is increasing at its market limit $N=S+M$ i.e., i.e., that $\frac{\beta}{2 \sqrt{p}\sqrt{S+M}} > (\alpha + p(\tau+c))$. When the multi-homing customer segment $M$ is small (hence the firm gives up a large number of customers who only visit the other platform), or conversion rate $p$ is low (and so it generates limited sales) then the single-homing approach is less attractive. The market reach $S+M$ (blue vertical dashed line) is more binding, yielding profit $\beta \sqrt{S+M} - (\frac{a}{p} + \tau+c)(S+M)$, which could possibly be improved by going it alone or multi-homing with both platforms.

2.3 Single- vs Multi-Homing for Discovery

Finally, let’s compare working with platforms for discovery, under both single- and multi-homing, and against the do-it-yourself possibility. Not surprisingly, now, multi-homing with both platforms is attractive when customers are predominantly single-homing (low $M$), because then the redundancy in discovery costs pales against the lost market under single-homing with one platform only. Second, single-homing is ideal with a large fraction of customers multi-homes (hence there is little sacrifice) and it dominates a do-it-yourself approach when the efficiency gain is high (low $a$ relative to $\alpha$). Looking at the figure, multi-homing becomes less attractive when discovery price paid to platform increases (move towards the bottom of figure) and when multi-homing poses a greater redundancy inefficiency due to high M (moving towards right). This supports the intuition that if a large group of customers is present on both platforms, then there is little value to the business in engaging the help of both platforms for customer discovery.

There are some issues that this analysis highlights.

Just because platforms might be more efficient at enabling discovery of potential buyers (than the traditional means available to the business), it doesn’t necessarily mean that the business should adopt them.
A platform even when big might not cover the market fully, thus the business should examine whether or not it can forego the remaining market segment (perhaps it is a small business, and at its scale there might be nothing lost if it can’t reach the whole market). In particular, this is a problem if a platform imposes exclusivity constraints on the business.
If there are multiple platforms, then the business needs to be aware of the redundancy costs involved in employing both platforms for customer discovery, particularly when a chunk of discovered customers are common on both platforms. This is less bothersome when more messaging can lead to more purchase (e.g., people spend more time on TV shows if they are subject to more advertising about them); but when demand quantity is capped (how much milk will you buy) then this is a cost to worry about.

2.4 Coming Ahead

So far the model does not exactly mirror what you might have found empirically – but that is because I introduced additional elements such as degree of single vs multi homing on user side; and the parameter p which tells you how frequently a discovery leads to actual sale (and this will become more relevant when we consider the business’s dealing with fulfillment platforms).

We assumed that the two platforms are symmetric in their discovery capability. And we assumed some level of single-homing and multi-homing among the customer side. One direction to consider is that i) platforms are asymmetric (one has better discovery cost than other) and ii) that customers single-home. Then, it would be good if the model implies that – the business multi-homes even when its total sales are less than the reach capacity of a single better platform.

3 Leveraging a Platform’s Fulfillment Services

Here we could consider that the business has a fixed cost $F$ of partnering with a fulfillment platform (e.g., integration of IT systems etc.), and that the cost of partnering with both platforms is $2^{\alpha} F$ (with $\alpha \in [0, 1]$, 0 value indicating that there is little extra cost to join the 2nd platform, and higher value indicating that the cost of two is double the cost of one).