The paradox and non-paradox of power for groups

Fixed numbers of agents equipped with high versus low fighting effort sort themselves into n groups. The group sizes and fractions of strong agents in each group are determined endogenously. The agents compete within and between the groups for their aggregate production which is fixed for the n groups. A paradox of power, with all strong agents in a small group and all weak agents in the large group, arises for a small group with high within-group decisiveness given that the large group has low within-group decisiveness and the between-group decisiveness is within a range. Conversely, the more common non-paradox of power, with all weak agents in a small group and all strong agents in the large group, arises for a small group with low within-group decisiveness given that the large group has high within-group decisiveness and the between-group decisiveness is within a range. As the between-group decisiveness becomes sufficiently large, one of the groups goes extinct regardless of the within-group decisiveness in the n groups.