This work adopts a game theoretic approach to analyze the behavior of transmitter nanomachines (TNMs) in a diffusive 3-dimensional (3-D) channel. In order to communicate the local observations about the region of interest (RoI) to a common supervisor nanomachine (SNM), TNMs transmit information-carrying molecules to SNM. For the production of information-carrying molecules, all the TNMs share the common food molecular budget (CFMB). The TNMs apply cooperative and greedy strategic efforts to get their share from the CFMB. In the cooperative case, all the TNMs communicate to SNM as a group, therefore they cooperatively consume the CFMB to increase the group outcome, whereas, in the greedy scenario, all TNMs decide to perform alone and thus greedily consume the CFMB to increase their individual outcomes. The performance is evaluated in terms of the average rate of success, the average probability of error, and the receiver operating characteristic (ROC) of RoI detection. The derived results are verified through Monte-Carlo and particle-based simulations (PBS).