Human activities often require simultaneous decision-making of individuals in groups. These processes cannot be coherently addressed by means of networks, as networks only allow for pairwise interactions. Here, we propose a general implementation for collective games in which higher-order interactions are encoded on hypergraphs. We employ it for the study of the public goods game by first validating the analytical expression of the replicator dynamics in uniform and heterogeneous populations, and then by introducing a procedure for retrieving empirical synergistic effects of group interactions from real datasets.