Horizon-K farsightedness in criminal networks

We study the criminal networks that will emerge in the long run when criminals are neither myopic nor completely farsighted but have some limited degree of farsightedness. We adopt the horizon-K farsighted set to answer this question. We find that in criminal networks with n criminals, the set consisting of the complete network is a horizon-K farsighted set whenever the degree of farsightedness of the criminals is larger than or equal to (n−1). Moreover, the complete network is the unique horizon-(n−1) farsighted set. Hence, the predictions obtained in case of completely farsighted criminals still hold when criminals are much less farsighted.