  Various conceptual and descriptive models of conversational search have been
proposed in the literature -- while useful, they do not provide insights into
how interaction between the agent and user would change in response to the
costs and benefits of the different interactions. In this paper, we develop two
economic models of conversational search based on patterns previously observed
during conversational search sessions, which we refer to as: Feedback First
where the agent asks clarifying questions then presents results, and Feedback
After where the agent presents results, and then asks follow up questions. Our
models show that the amount of feedback given/requested depends on its
efficiency at improving the initial or subsequent query and the relative cost
of providing said feedback. This theoretical framework for conversational
search provides a number of insights that can be used to guide and inform the
development of conversational search agents. However, empirical work is needed
to estimate the parameters in order to make predictions specific to a given
conversational search setting.
