Before revision:  Here, we consider several natural parameters such as the number of layers,  number of agents,  number of items, and maximal length of a preference list ; we present a comprehensive picture of the parameterized complexity of the problem with respect to these parameters.
After revision:  Here, we consider several natural parameters such as the number of layers, number of agents, number of items, and maximal length of a preference list . We present a comprehensive picture of the parameterized complexity of the problem with respect to these parameters.