Equilibrium analysis for platform developers in two-sided market with backward compatibility

We consider a dominant platform provider operating both legacy and new platforms that connects users with suppliers in a two-sided market context. In addition to the typical indirect network effects in the two-sided market, backward compatibility works on the new platform. Thus, users joining the new one can also enjoy the services provided by suppliers using the legacy platform. Users and suppliers are linearly differentiated between two platforms as in the Hotelling model and play a subscription game of choosing one platform at the lower level. The suppliers in the new platform may suffer from congestion, which can be alleviated by platform provider's investment on the new one. The platform provider also determines price margins for the supplier sides. Our equilibrium (eq.) analysis in the subscription game identifies an interior eq. (coexistence of both platforms in both sides). Though the backward compatibility plays a stabilizing role for the interior eq., its stability is fragile due to the network effects. Rather, some boundary eq.'s, where at least one side tips to the legacy or the new platform, are more likely to be stable. The backward compatibility is a key factor that characterizes the stable boundary eq.'s. The upper stage game is led by the platform provider, which tries to maneuver the system toward one of the stable boundary eq.'s using price margins and investment. The platform provider prefers an all-new boundary eq. when the indirect network effect and the maximum price margin for the new platform are large; thus, it puts a significant investment in the new one. With a small indirect network effect for suppliers, however, the platform provider does not invest in the new platform and choose a separate boundary eq. where two sides split into different platforms. Whether the user side completely tips to the new one (completely separated eq.) or not (partially separated eq.) depends on the backward compatibility. The relative advantage of the all-new eq. over the separate eq.'s in terms of social welfare from both sides depends on the backward compatibility as well as the indirect network effects for the new platform.