In this paper we propose a number of principles and conjectures for mixed-i
nitiative collaborative dialogs. We explore some methodologies for managing
initiative between conversational participants. We mathematically analyze
specific initiative-changing mechanisms based on a probabilistic knowledge
base and user model. We look at the role of negotiation in managing initiat
ive and quantify how the negotiation process is useful toward modifying use
r models. Some experimental results using computer-computer simulations are
presented along with some discussion of how such studies are useful toward
building human-computer systems.