In this paper, we consider the problem of scheduling independent jobs when several agents compete to perform their jobs on a common single processing machine. Each agent wants to minimise its cost function, which depends exclusively on its jobs and we assume that a global cost function concerning the whole set of jobs has to be minimised. This cost function may correspond to the global performance of the workshop or to the global objective of the company, independent of the objectives of the agents. Classical regular objective functions are considered and both the ε-constraint and a linear combination of criteria are used for finding compromise solutions. This new multi-agent scheduling problem is introduced into the literature and simple reductions with multicriteria scheduling and multi-agent scheduling problems are established. In addition, the complexity results of several problems are proposed and a dynamic programming algorithm is given.