In this paper, we propose a game-theoretic framework for analysing competing double auction marketplaces that vie for traders and make profits by charging fees. Firstly, we analyse the equilibrium strategies for the traders’ market selection decision for given market fees using evolutionary game theory. Using this approach, we investigate how traders dynamically change their strategies, and thus, which equilibrium, if any, can be reached. In so doing, we show that, when the same type of fees are charged by two marketplaces, it is unlikely that competing marketplaces will continue to co-exist when traders converge to their equilibrium market selection strategies. Eventually, all the traders will congregate in one marketplace. However, when different types of fees are allowed (registration fees and profit fees), competing marketplaces are more likely to co-exist in equilibrium. We also find that sometimes all the traders eventually migrate to the marketplace that charges higher fees. We then further analyse this phenomenon, and specifically analyse how bidding strategies and random exploration of traders affects this migration respectively. Secondly, we analyse the equilibrium strategies of the marketplaces when they have the ability to vary their fees in response to changes in the traders’ market selection strategies. In this case, we consider the competition of the marketplaces as a two-stage game, where the traders’ market selection strategies are conditional on the market fees. In particular, we use a co-evolutionary approach to analyse how competing marketplaces dynamically set fees while taking into account the dynamics of the traders’ market selection strategies. In so doing, we find that two identical marketplaces undercut each other, and they will eventually charge the minimal fee as we set that guarantees positive market profits for them. Furthermore, we extend the co-evolutionary analysis of the marketplaces’ fee strategies to more general cases. Specifically, we analyse how an initially disadvantaged marketplace with an adaptive fee strategy can outperform an initially advantaged one with a fixed fee strategy, or even one with an adaptive fee strategy, and how competing marketplaces evolve their fee strategies when different types of fees are allowed.