Hmmm, you raise an interesting question. I'm no game theorist, but are bully/victim dynamics and Nash equilibria necessarily mutually exclusive? What I'm getting at is: the threat of force determines every other player's optimal strategy, with a fight always being the last resort for everyone involved.
Under such conditions, Adam giving the bully his lunch money, Bob his homework, and Charlie his lunch may be the Nash equilbrium—that is, until Dave (who knows kung fu) moves to the neighborhood.
Under such conditions, Adam giving the bully his lunch money, Bob his homework, and Charlie his lunch may be the Nash equilbrium—that is, until Dave (who knows kung fu) moves to the neighborhood.