This paper investigates the structure of the payment card market, with consumers and merchants basing their subscription decisions on different information sets. We find that the market structure depends crucially on the information set on which consumers and merchants base their subscription decisions. In the studied case, we observe that a market with few cards dominating only emerges when decisions are based on very limited information. Under the same conditions using a complete information set, all cards survive in the long run. The use of an agent-based model, focusing on the interactions between merchants and consumers, as a basis for subscription decisions allows us to investigate the dynamics of the market and the effect of the indirect network externalities rather than investigating only equilibrium outcomes.