The current study explored whether the social exchange heuristic (SEH) hypothesis would hold for trust behavior. In previous studies, using prisoner’s dilemma games (PDG), the cooperation rate in the partner-specified condition, in which the interaction partner was determined before decision-making, was higher than in the partner-unspecified condition, in which the partner was not determined, supporting the SEH hypothesis. However, the SEH hypothesis has rarely been tested in other economic games, and it remained unclear whether this would also explain other behaviors. Thus, we tested the SEH hypothesis using a trust game (TG) and a faith game (FG). We manipulated the partner-specificity in an online experiment and found that trust behavior was not influenced by the manipulation either in the TG or the FG. In contrast, a similar experiment with a PDG revealed that cooperation was higher in the partner-specified condition than in the partner-unspecified condition, replicating previous findings. These results suggest that the SEH may not be activated in the TG and FG.