  We introduce a model of dyadic social interactions and establish its
correspondence with relational models theory (RMT), a theory of human social
relationships. RMT posits four elementary models of relationships governing
human interactions, singly or in combination: Communal Sharing, Authority
Ranking, Equality Matching, and Market Pricing. To these are added the limiting
cases of asocial and null interactions, whereby people do not coordinate with
reference to any shared principle. Our model is rooted in the observation that
each individual in a dyadic interaction can do either the same thing as the
other individual, a different thing or nothing at all. To represent these three
possibilities, we consider two individuals that can each act in one out of
three ways toward the other: perform a social action X or Y, or alternatively
do nothing. We demonstrate that the relationships generated by this model
aggregate into six exhaustive and disjoint categories. We propose that four of
these categories match the four relational models, while the remaining two
correspond to the asocial and null interactions defined in RMT. We generalize
our results to the presence of N social actions. We infer that the four
relational models form an exhaustive set of all possible dyadic relationships
based on social coordination. Hence, we contribute to RMT by offering an answer
to the question of why there could exist just four relational models. In
addition, we discuss how to use our representation to analyze data sets of
dyadic social interactions, and how social actions may be valued and matched by
the agents.
