An independent dominating set (IDS) is a set of vertices in a graph that ensures both independence and domination. The former property asserts that no vertices in the set are adjacent to each other while the latter demands that every vertex not in the set is adjacent to at least one vertex in the IDS. We extended two prior game designs, one for independent set and the other for dominating set, to three IDS game designs where players independently determine whether they should be in or out of the set based on their own interests. Regardless of the game play sequence, the result is a minimal IDS (i.e., no proper subset of the result is also an IDS). We turned the designs into three self-stabilizing distributed algorithms that always end up with an IDS regardless of the initial configurations. Simulation results show that all the game designs produce relatively small IDSs with reasonable convergence rate in representative network topologies.