  Social hierarchy in animal groups carries a crucial adaptive function by
reducing conflict and injury while protecting valuable group resources. Social
hierarchy is dynamic and can be altered by social conflict, agonistic
interactions, and aggression. Understanding social conflict and aggressive
behavior is of profound importance to our society and welfare. In this study,
we developed a quantitative theory of social conflict. We modeled individual
agonistic interactions as a normal-form game between two agents. We assumed
that the agents use Bayesian inference to update their beliefs about their
strength or their opponent's strength and to derive optimal actions. We
compared the results of our model to behavioral and whole-brain neural activity
data obtained for a large (n=116) population of mice engaged in agonistic
interactions. We find that both types of data are consistent with the
first-level Theory of Mind model (1-ToM) in which mice form both "primary"
beliefs about their and their opponent's strengths as well as the "secondary"
beliefs about the beliefs of their opponents. Our model helps identify brain
regions that carry information about these levels of beliefs. Overall, we both
propose a model to describe agonistic interactions and support our quantitative
results with behavioral and neural activity data.
