We analyze how network effects affect competition in the nascent cryptocurrency market. We do so by examining the changes over time in exchange rate data among cryptocurrencies. Specifically, we look at two aspects: (1) competition among different currencies, and (2) competition among exchanges where those currencies are traded. Our data suggest that the winner-take-all effect is dominant early in the market. During this period, when Bitcoin becomes more valuable against the U.S. dollar, it also becomes more valuable against other cryptocurrencies. This trend is reversed in the later period. The data in the later period are consistent with the use of cryptocurrencies as financial assets (popularized by Bitcoin), and not consistent with winner-take-all dynamics.