of a lack of response have not been required. For example, Horvitz's (1999) work using decision theory is aimed at developing general, theoretical models for AA reasoning for a user at a workstation. A prototype system, called Look Out, for helping users manage their calendars has been implemented to test these ideas (Horvitz, 1999). Although such systems are distinctly different from E-Elves, mapping them to our problem formulation allows us to analyze the utility of the approaches across a range of domains without having to implement the approach in those domains.

A critical difference between Horvitz's work and our work is that LookOut does not address the possibility of not receiving a (timely) response. Thus, complex strategies are not required. In the typical case for Look Out, the agent has three options: to take some action, not to take the action, or to engage in dialog. The central factor influencing the decision is whether the user has a particular goal that the action would aid, i.e., if the user has the goal, then the action is useful, but if he/she does not have the goal, the action is disruptive. Choosing to act or not to act corresponds to pursuing strategy A. 7 Choosing to seek user input corresponds to strategy U. Figure 17(a) shows a graph of the different options plotted against the probability the user has the goal (corresponds to Figure 6 in Horvitz (199)). The agent's expected decision quality, EQ f ( t ) is derived from Equation 2 in Horvitz (1999). (In other words, Horvitz's model performs more detailed calculations of expected decision quality.) Our model then predicts the same selection of strategies as Horvitz does, i.e., choosing strategy A when EQ a (t) is low, U otherwise (assuming that only those two strategies are available). However, our model further predicts something that Horvitz did not consider, i.e., that if the rate at which wait costs accrue becomes nn-negligible then the choice is not as simple. Figure 17(b) shows how the EU of the two strategies changes as the rate of wait costs accruing is increased. The fact that the optimal strategy varies with wait cost suggests that Horvitz's approach would not immediately be appropriate for a domain where wait costs were non-negligible, e.g., it would need to be modified in many multi-agent settings.

## 6.2  Other Approaches To Aa

Several different approaches have been taken to the core problem of whether and when to transfer decision-making control. For example, Hexmoor examines how much time the agent has to do AA reasoning (Hexmoor, 2000). Similarly, in the Dynamic Adaptive Autonomy framework, a group of agents allocates votes amongst themselves, hence defining the amount of influence each agent has over a decision and thus, by their definition, the autonomy of the agent with respect to the decision (Barber, Martin, & Mckay, 2000b). For the related application of meeting scheduling Cesta, Collia, and D'Aloisi (1998) have taken the approach of providing powerful tools for users to constrain and monitor the behavior of their proxy agents, but the agents do not explicitly reason about relinquishing control to the user. While at least some of this work is done in a multiagent context, the possibility of multiple transfers of control is not considered.

Complementing our work, other researchers have focused on issues of architectures for A. For instance, an AA interface to the 3T architecture (Bonasso, Firby, Gat, Kortenkamp,