Many cryptographic protocols aim at ensuring the route validity in ad-hoc networks, i.e. the established route representing an exists path in the network. However, flaws have been found in some protocols that are claimed secure (e.g. the attack on SRP applied to DSR). Some formal models and reduction proofs have been proposed to give more guarantees when verifying route validity and facilitate verification process. The existing approaches assume the cooperative attacker model. In this paper, we consider the non-cooperative attacker model, and we show that verifying the route validity under the non-cooperative model requires to verify only five topologies, each containing four nodes, and to consider only three malicious (compromised) nodes. Furthermore, we prove that a protocol is secure for any topology under the non-cooperative model, if and only if, it is secure for any topology under the cooperative model.