Are there "winner-takes-it-all" effects in blockchain user adoption?

There are many blockchain and token platforms with varying success when it comes to sustained user adoption. This paper investigates whether some of these platforms are more likely to dominate others in the long-run, i.e., whether there are ``winner-takes-it-all'' effects or whether adoption shares become stable. Our theory predicts that we may observe both positive and negative network effects in the short-run, but adoption share sequences behave like martingales in the limit and thus, achieve stability. This result arises from the fact that more (less) adopted user platforms tend to have a lower (higher) likelihood of capturing significant fractions of growing user numbers and that adoption rate sequences converge to their sample mean in the limit. We further characterize the limiting distribution of adoption shares and provide a framework to test for martingale properties. Empirically, we test whether some of the existing platforms' user adoption shares behave like martingales. We find that three blockchains in our sample do not reject our martingale hypothesis while others do not (yet) behave like martingales due to limited information content and shorter transaction history. We then apply our framework to token platforms and find that many token categories have reached stability in terms of adoption shares. Other token categories exhibit patterns of persistent increases (decreases) in adoption shares, pointing to positive (negative) network effects, rather than stability. In such cases, our (theoretical) framework can be applied to test the martingale hypothesis and see whether stability has been reached at a later date.