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Upstart Puzzles: Strategic Friendship


Strategic Friendship, illustration

Consider the following game (first posed to my close friend Dr. Ecco) played among several entities. Each entity Ei has a certain force Fi and a certain wealth Wi. A coalition of one or more entities has a combined force equal to the sum of the force of the individual entities. If a coalition C1 has a force that exceeds the force of a coalition C2, and C1 attacks C2, then C2 is eliminated, and the wealth of the entities making up C2 is distributed equally among the coalition members of C1, but the force of the coalition members in C1 does not change. Note every member of a coalition must agree to attack for an attack to take place. If the force of C1 is less than the force of C2, and C1 attacks C2, then C1 is eliminated. This will never happen, however, because we assume every entity wants to survive and increase its wealth. If the force of C1 is equal to the force of C2, then an attack has no effect.

Starter warm-up 1. Suppose there are only two entities—E1 and E2—and F1 > F2. What happens then?


 

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