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In this paper, we introduce a distributed dynamic routing algorithm for secondary users (SUs) to minimize their interference with the primary users (PUs) in multi-hop cognitive radio (CR) networks. We use the medial axis with a relaxation factor as a reference path which is contingent on the states of the PUs. Along the axis, we construct a hierarchical structure for multiple sources to reach cognitive pilot channel (CPC) base stations. We use a temporal and spatial dynamic non-cooperative game to model the interactions among SUs as well as their influences from PUs in the multi-hop structure of the network. A multi-stage fictitious play learning is used for distributed routing in multi-hop CR networks. We obtain a set of mixed (behavioral) Nash equilibrium strategies of the dynamic game in closed form by backward induction. The proposed algorithm minimizes the overall interference and the average packet delay …