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

There are many public blockchains with various levels of success when it comes to sustained user adoption. This paper investigates whether some blockchains are more likely to dominate others in the long-run, i.e., whether there are "winner-takes-it-all" dynamics or whether a blockchain's adoption shares become stable. Our theory predicts that, although we may observe both positive and negative network effects in the short-run, user adoption share sequences behave like martingales in the limit and thus, achieve stability. This result arises from the fact that more (less) adopted blockchains 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. Empirically, we test whether some of the existing public blockchains' adoption shares behave like martingales. Two of the oldest blockchains in our sample, Bitcoin and Litecoin, do not reject our martingale hypothesis while others do not (yet) behave like martingales due to limited information content and length of their transaction history. Finally, Bayesian users update their beliefs about the distribution of adoption shares over time and are thus better able to make adoption decisions regarding those blockchains that already behave like martingales