The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two teams playing according to a small set of simple rules, taking place on four types of complex networks. Starting from a minimalist game, characterized by full symmetry always leading to ties, four other games are described in progressive order of complexity, taking into account the presence of neighbors as well as strategies. Each of these five games, as well as their specific changes when implemented in four types of networks, are studied in terms of statistics of the total duration of the game as well as the number of victories and ties, with several interesting results that substantiate, in some cases, the importance of the network topology on the respective dynamics. As a subsidiary result, the visualization of relationships between the data elements in terms of coincidence similarity networks allowed a more complete and direct interpretation of the obtained results.