The relevance of bargaining to everyday life can easily be ascertained, yet the study of any bargaining process is extremely hard, involving a multiplicity of questions and complex issues. The objective of this paper is to provide new insights on some dimensions of the bargaining process - asymmetries and uncertainties in particular - by using a non-cooperative game theory approach. We develop a computational model which simulates the process of negotiation among more than two players, who bargain over the sharing of more than one pie. Through numerically simulating several multiple issues negotiation games among multiple players, we identify the main features of players' optimal strategies and equilibrium agreements. As in most economic situations, uncertainty crucially affects also bargaining processes. Therefore, in our analysis, we introduce uncertainty over the size of the pies to be shared and assess the impact on players' strategic behaviour. Our results confirm that uncertainty affects players' behaviour and modify the likelihood of a self-enforcing agreement to emerge. The model proposed here can have several applications, in particular in the field of natural resource and environmental management at the national or local level, where conflicts over how to share a resource of a finite size are increasing. (c) 2008 Elsevier Ltd. All rights reserved.