The primate prefrontal cortex represents both past and future goals. To investigate its role in representing the goals of other agents, we designed a nonmatch-to-goal task that involved a human-monkey (H-M) interaction. During each trial, 2 of 4 potential goal objects were presented randomly to the left or right part of a display screen, and the monkey's (or human's) task was to choose the one that did not match the object goal previously chosen. Human and monkey trials were intermixed, and each agent, when acting as observer, was required to monitor the other actor's choice to switch the object goal choice in case it became the actor on the subsequent trial. We found neurons encoding the actor, either the monkey itself or the human, neurons encoding the agent future goal position and neurons encoding the agent previous goal position. In the category of neurons encoding the human future goal, we differentiated between those encoding the future goal of both agents and those encoding only the human agent future goal. While the first one might represent a covert mental simulation in the human trials, the other one could represent a prediction signal of the other's agent choice.