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Weakly-supervised semantic segmentation (WSSS) methods, reliant on image-level labels indicating object presence, lack explicit correspondence between labels and regions of interest (ROIs), posing a significant challenge. Despite this, WSSS methods have attracted attention due to their much lower annotation costs compared to fully-supervised segmentation. Leveraging reinforcement learning (RL) self-play, we propose a novel WSSS method that gamifies image segmentation of a ROI. We formulate segmentation as a competition between two agents that compete to select ROI-containing patches until exhaustion of all such patches. The score at each time-step, used to compute the reward for agent training, represents likelihood of object presence within the selection, determined by an object presence detector pre-trained using only image-level binary classification labels of object presence. Additionally, we propose a game termination condition that can be called by either side upon exhaustion of all ROI-containing patches, followed by the selection of a final patch from each. Upon termination, the agent is incentivised if ROI-containing patches are exhausted or disincentivised if a ROI-containing patch is found by the competitor. This competitive setup ensures minimisation of over- or under-segmentation, a common problem with WSSS methods. Extensive experimentation across four datasets demonstrates significant performance improvements over recent state-of-the-art methods. Code: https://github.com/s-sd/spurl/tree/main/wss.