There is already IAM(Information adoption model), but it is not suitable enough in the context of dialogue. So, I wonder if there is a theory or model to describe information adoption in a dialogue.
You might want to start with B.A. Fisher (1978). Perspectives on human communication. MacMillan Publishing CO. Inc. Describes human communication process and analyses four perspectives: Mechanistic ( how are data send and received technically and instrumental, and what distortions can exist) Psychological ( what mindset is required and what are principles of eg the will to understand each other like attentiveness to sender, willingness to listen)
Symbolic interactional (e.g. what symbols are used for what senses (e.g. alphabet, characters, icons, morse code)
Pragmatic: what effect does human communication actually have on behaviour.
Some work never goes out of date, and some research is principally biased because of setting a too short time limit to scientific literature to be included.
Professor Luc Steels has studied the system made by two robots/machines in dialogue, agreeing concepts after negotiation. This is a dialogue for collaborative and iterative language definition see here https://scholar.google.es/citations?user=T7RihQEAAAAJ&hl=en
Hi - I am not aware of such a theory, but I did come across this paper about the adoption of acronyms in various communitees. It may be of use to you (even if it's just to decide it's not useful).
It's right at the edge of my research interests, far from central and I have not included any of it's ideas in my own research (it's one I crossed off my list) but it may be of use to you.
Article Emergence of Acronyms in a Community of Language Users
Peter Checkland (Checkland, P. (1984/1993). Systems thinking, systems practice. Chichester, John Wiley & Sons Ltd.) writes about how to analyse a human activity system, identify expressed problems, compare possible solutions with a model, improve the situation based on feasible and desirable changes. For that a rational approach can deal for instance with the information (system). But also he points at a cultural stream that does focus on adaptation of the understanding of the system, its problem, its improvements and whether it is desirable. If does not answer your detailed question, but does give a good context for it, in particular since the dialogue about desirability has to be done with each stakeholder.