By observing their social partners, primates learn about reward values of objects. Here, we show that monkeys' amygdala neurons derive object values from observation and use these values to simulate a partner monkey's decision process. While monkeys alternated making reward-based choices, amygdala neurons encoded object-specific values learned from observation. Dynamic activities converted these values to representations of the recorded monkey's own choices. Surprisingly, the same activity patterns unfolded spontaneously before partner's choices in separate neurons, as if these neurons simulated the partner's decision-making. These "simulation neurons" encoded signatures of mutual-inhibitory decision computation, including value comparisons and value-to-choice conversions, resulting in accurate predictions of partner's choices. Population decoding identified differential contributions of amygdala subnuclei. Biophysical modeling of amygdala circuits showed that simulation neurons emerge naturally from convergence between object-value neurons and self-other neurons. By simulating decision computations during observation, these neurons could allow primates to reconstruct their social partners' mental states.