Trust is an important concept that intersects a number of different disciplines, including economics, sociology, and political science, and maintains some meaning even in the natural sciences. Any situation where non-simultaneous exchanges between living organisms take place involves a problem of trust. We used computer simulations to study the evolution of trust in non-simultaneous exchange situations formalized by means of a Trust game. We found that trust and reciprocity-based cooperation are likely to emerge only when agents have the possibility of building trustworthy reputations and when the information regarding agents’ past behaviors is sufficiently spread in the system. Both direct and indirect reciprocity play a role in fostering cooperation. However, the strength of the latter is greater under most of the examined conditions. In general, our findings are consistent with theories arguing for a positive feedback relationship between trust, reputation, and reciprocity, leading together to higher levels of cooperation.