The neural underpinning of cooperative and competitive constructive activity has been investigated using mass-univariate approaches. In this study, we sought to compare the results of these approaches with the results of multivariate pattern analysis (MVPA). In particular, we wanted to test whether MVPA supports the claim made in previous studies that cooperation is associated with the activity of reward-related brain circuits. Participants were required to construct a pattern on the screen either individually or in cooperation or competition with another person during an fMRI scan. Both the MVPA classification methods and the representational similarity analysis indicated the involvement of orbitofrontal and ventromedial prefrontal areas in processes that distinguish between cooperation and competition, and activation analysis showed that these areas are more active during cooperation than during competition. However, a single trial analysis showed that the effect was reversed when only winning trials were considered. In these trials, activation of reward-related areas was higher during competition than during cooperation. Moreover, the contrast between won and lost trials in terms of reward circuits involvement was sharper under competition than under cooperation. Thus, although cooperation can be generally more rewarding than competition, it is associated with smaller difference between trials lost and trials won in terms of reward circuits activation. One may speculate that in cooperation, victory and defeat are shared with the partner and, contrary to competition, are not experienced as personal achievement or failure.