We present a novel resilient routing policy for controlling the routing across peering links between Internet carriers. Our policy is aimed at offering more dependability and better performance to the routing decision with respect to the current practice (e.g., hot-potato routing). Our work relies on a non-cooperative game framework, called Peering Equilibrium MultiPath (PEMP), that has been recently proposed. PEMP allows two carrier providers to coordinate a multipath route selection for critical flows across peering links, while preserving their respective interests and independence. In this paper, we propose a resilient PEMP execution policy accounting for the occurrence of potential impairments (traffic matrix variations, intra-AS and peering link failures) that may occur in both peering networks. We mathematically define how to produce robust equilibrium sets and describe how to appropriately react to unexpected network impairments that might take place. The results from extensive simulations show that, under a realistic failure scenario, our policy adaptively prevents from peering link congestions and excessive route deviations after failures.