Reciprocity is an important factor in human–human interaction, so it can be expected that it should also play a major role in human–robot interaction (HRI). Participants in our study played the Repeated Prisoner’s Dilemma Game (RPDG) and the mini Ultimatum Game (mUG) with robot and human agents, with the agents using either Tit for Tat (TfT) or Random strategies. As part of the study we also measured the perceived personality traits in the agents using the TIPI test after every round of RPDG and mUG. The results show that the participants collaborated more with humans than with a robot, however they tended to be equally reciprocal with both agents. The experiment also showed the TfT strategy as the most profitable strategy; affecting collaboration, reciprocation, profit and joint profit in the game. Most of the participants tended to be fairer with the human agent in mUG. Furthermore, robots were perceived as less open and agreeable than humans. Consciousness, extroversion and emotional stability were perceived roughly the same in humans and robots. TfT strategy became associated with an extroverted and agreeable personality in the agents. We could observe that the norm of reciprocity applied in HRI has potential implications for robot design.