This paper analyses the motivation and strategies for ensuring cooperative behaviour among hosts and customer networks in the Internet and 5G networks. The hypothesis is that better cooperation among the benevolent entities could improve the overall Internet welfare, motivating the need for adoption of cooperative security. However, in state-of-the-art, the prevalent security approach in the Internet is based on self-help, while the adoption of cooperative methods is progressing slowly. At the same time, the ubiquitous reliance on 5G and mission critical nature of some of the new services, for example, ultra-reliable (machine-to-machine) communication and Internet of Things, requires that 5G will do its best to curb the malicious (non-cooperative) behaviour from becoming a cause of failure to the legitimate services. In this paper, we relate our analysis of the conditions for sustainable cooperation in the Internet with the famous end-to-end principle, and present the hypothesis that there is no end-to-end solution to the problem of ensuring cooperation among Internet hosts. Game theory allows studying the outcomes of interactions among the players with conflicting interests. We use it to study the hypothesis, and show that introducing the reputation of Internet nodes and customer networks can lead to cooperation, which improves the overall Internet welfare and reduces the payoffs of malicious actors. We study the possible response of non-cooperative users with advanced defection strategies and the resulting outcomes. We argue that 5G shall make significant progress towards uprooting the selfish behaviour and malicious activities using cooperation and relate it with motivation for providing ubiquitous connectivity and ultra-reliable services. The paper concludes by summarizing our earlier work on the application of the proposed methods of cooperation to 5G and the Internet; outlining how cooperation in security is not only desirable but also feasible.