Sequential decision-making in a dynamic environment requires foresight into future states often influenced by other agents. This study seeks to uncover the neural correlates underlying the computation of self and opponent action values in the brain. To achieve this, rhesus monkeys were trained in a competitive strategy board game, called “four-in-a-row,” in which they placed a series of stones on a 4-by-9 board, taking turns with a computer opponent. In this game, players win by placing a series of four stones horizontally, vertically, or diagonally, and the animal was rewarded only for winning. Neural recordings were performed in one or two brain areas among the dorsomedial prefrontal cortex, dorsolateral prefrontal cortex, and caudate nucleus.The present analysis focused on evaluating neural signals related to the value of the board positions selected by each player. We used the maximal number of stones connected by the current move (referred to as connection length) as a proxy for the value of the player’s move. We found that neurons in the prefrontal cortex and caudate nucleus often modulated their activity according to the connection lengths of both players. In addition, the cross-correlation analysis of the regression coefficients related to the connection lengths of both players indicated that the values of the two players are temporally multiplexed in the prefrontal cortex and caudate nucleus. These results suggest that the prefronto-striatal system contributes to computing the value of alternative actions during iterative social interactions.