We study the complexity of a multilateral negotiation framework where autonomous agents agree on a sequence of deals to exchange sets of discrete resources in order to both further their own goals and to achieve a distribution of resources that is socially optimal. When analysing such a framework, we can distinguish different aspects of complexity: How many deals are required to reach an optimal allocation of resources? How many communicative exchanges are required to agree on one such deal? How complex a communication language do we require? And finally, how complex is the reasoning task faced by each agent? This paper presents a number of results pertaining, in particular, to the first of these questions.