[Research] Still trying to sketch a better definition of mutual modeling

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I am trying to define mutual modeling as something more process-oriented. I defined it earlier as the "representation of the partner cognitive state, namely inferences an individual make about his/her partner’s goals, purposes, intents, understanding". Now that I read some claims about Sperber and Wilson (1986), I would say that mutual modeling includes 2 processes

  1. awareness: monitoring other's (activities)
  2. interpreting (inferring?) theses facts as (i) relevant, (ii) manifest for the joint activity carried out by the group.

but what about mutual influencing, perspective taking, mutual modeling?????