In schoolyards, the world of crime, and international affairs, certain entities try to take valuables from others by force. They attack most happily when they have overwhelming power and the target is wealthy. Sometimes individuals or groups join forces, forming a temporary coalition to gain wealth or to deter an attack.

Let's assume that the following rules hold. An entity's power is represented by a number; if the entity is a coalition, the coalition's power is equal to the sum of its members' powers; wealth is proportional to power. Entity A will attack B only if A is sure of winning (if A's power is greater than B's). When an entity is beaten, the winners gain its wealth but not its power. Every entity plays selfishly, striving to acquire riches yet avoid certain destruction. A configuration of power values is said to be stable if no fighting will occur--as will happen if a coalition can form that is strong enough to prevent fighting and if being loyal to the coalition is in every member's best interests.

This article was originally published with the title Strategic Bullying.

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