The enemy of my enemy is my friend is the enemy: Dealing with the war-provoking rules of intent

A set of rules often invoked to explain or justify the evolution of intentions and the consequent behavior of competitive systems consists of the following: 1. The friend of my friend is my friend. 2. The friend of my enemy is my enemy. 3. The enemy of my firiend is my enemy. 4. The enemy of my enemy is myfiriend. These rules have been modeled as a set of nonlinear coupled differential equations from which predictions can be derived as to eventual alliance building or conflict in the system, predictions which are quite ominous for the behavior of simple three-body systems. This paper presents illustrations of the application of the rules to international behavior and discusses the relationship between the rules as usually verbally applied and the associated mathematical models. Not all of these rules are equally desirable: behavior in accordance to the fourth rule has led to major difficulties in the "real world." This fourth rule cannot just be dropped, since the four rules are not independent of each other in the mathematical model. Hence the model must be altered. A simple mathematical modification is suggested which implies increased flexibility in the verbal statement and application of the rules; e.g., the fourth now reads "The enemy of my enemy may be my friend." The altered model leads to altered predictions of the evolution of intent which are much less ominous for the outcome of three-body competitions.