In this paper, we propose a novel general framework for analysing competing double auction markets that vie for traders, who then need to choose which market to go to. Based on this framework, we analyse the competition between two markets in detail. Specifically, we game-theoretically analyse the equilibrium behaviour of traders’ market selection strategies and adopt evolutionary game theory to investigate how traders dynamically change their strategies, and thus, which equilibrium, if any, can be reached. In so doing, we show that it is unlikely for these competing markets to coexist. Eventually, all traders will always converge to locating themselves at one of the markets. Somewhat surprisingly, we find that sometimes all traders converge to the market that charges higher fees. Thus we further analyse this phenomenon, and specifically determine the factors that affect such migration.