Isolation and exploitation of minority: Game theoretical analysis

We investigate various group-size distributions occurring in a situation where each group's resource is exposed to appropriation by other groups. The amount of appropriation depends on the size difference between groups. Our work focuses on the cases where the entire community isolates a small group or even an individual to maximize its gain. While people's basic motivation to form a group can be understood based on the group-size effect on multiplying a collective asset, sensitive factors that induce a asymmetric group distribution are the group efficiency and the ratio of secured assets to assets pending in a competition. We show that social rejection to a minor group may occur when the group efficiency is relatively low and their asset is severely exposed to possible appropriation.