CLV than the other). Yet our analysis shows that even when products are similar in terms of their profitability drivers, firms may still have a motivation to transfer customers. A Platform Benefit Model We use a fundamental approach to CLV modeling, where the CLV of an individual can be represented as (1) , which in the case of infinite horizon, sums to (2) . Whereby r is the individual-level retention probability per period t; P is a fixed gross profit per period; and d is the discount rate (Kumar and Pansari 2015; Kumar, Ramani, and Bohling 2004). We consider a two-product platform in which Product 1 is introduced at Period 1 and continues after the introduction of Product 2 that occurs at Period T+1. Thus, before Period T, only one product is available that belongs to the platform, while from Period T+1 onwards, two products are available (see Figure 1). Figure 1: Product Platform with two Games We assume that between t = 1 and t = T, customers of Product 1 can only externally (out of the platform), while from period t = T+1 onwards, customers of Product 1 can churn externally (out of the platform) and internally (to Product 2). Customers of Product 2 can churn externally only, as we do not include a third product in the platform. That being said, it is straightforward to construct a multi-product platform along the same lines mutatis mutandis – see
user of Product 2 is then . In both cases, the gross profit per period generated in T+2 is P, which needs to be discounted accordingly. The last row of Table 2 sums the value created in the platform by both products. The exact set of transferal and retention events from one product to the next is detailed in Appendix A. Given that the gross profit per period is constant over time and identical for both products, it is easy to show that summing up the value created by both products from Period 1 to infinity results in the standard CLV of formula (Equation 2) with retention rate . Specifically, the total value does not depend upon the internal retention . For two similar products with constant and identical gross profit per period, cross promotion that will result in customer transferal does not create additional value. The Case of Changing Gross Profit per Period The aforementioned picture becomes more complex when customer profitability changes over time. To better understand how such a change affects overall platform profitability, we need to look at the two factors that drive CLV – retention probability and per period profitability – and how these factors may change over time. To answer the question of a change in individual retention probability over time, it is necessary to carefully distinguish between cohort and individual-level change. At the cohort level, average retention rates will increase over time even if at the individual level, customer retention remains stable. This is due to heterogeneity among customers in their retention rates under which lower-retention customers leave early (Fader and Hardie 2010), pushing up the average retention rate at the cohort level among the remaining customers. Consequently, a
decline per period () 49.0% 39.5% Platform benefit (Equation 4) 27.6% 24.4% Elasticity: % improvement per 1% of increased cross promotion () 1.4% 1.3% Elasticity: % improvement per 1% of increased external retention () 0.7% 0.5% Change in platform benefit if cross promotion decreases from 16.5% to 10% -9.9% -9.0%