This paper analyses the process and outcomes of competitive bilateral negotiation for a model based on negotiation decision functions. Each agent has time constraints in the form of a deadline and a discounting factor. The importance of information possessed by participants is highlighted by exploring all possible incomplete information scenarios - both symmetric and asymmetric. In particular, we examine a range of negotiation scenarios in which the amount of information that agents have about their opponent’s parameters is systematically varied. For each scenario, we determine the equilibrium solution and study its priorities. The main results of our study are as follows. Firstly, in some scenarios agreement takes place at the earlier deadline, while in others it takes place near the beginning of negotiation. Secondly, in some scenarios the price surplus is split equally between the agents while in others the entire price surplus goes to a single agent. Thirdly, for each possible scenario, the equilibrium outcome possesses the properties of uniqueness and symmetry - although it is not always Pareto optimal. Finally, we also show the relative impacts of the opponent’s parameters on the bargaining outcome.