Multiple colour interacting urns on complete graphs

We present a multiple colour generalisation of the model of graph interacting urns studied by Benaim et. al., Random Struct. Alg., 46: 614-634, 2015. We show that for complete graphs and for a broad class of reinforcement functions governing the addition of balls in the urns, the process of colour proportions at each urn converges almost surely to the fixed points of the reinforcement function.