We model radicalization in a society consisting of two competing religious, ethnic or political groups. Each of the ‘sects’ is divided into moderate and radical factions, with intragroup transitions occurring either spontaneously or through indoctrination. We also include the possibility of one group violently attacking the other. The intra-group transition rates of one group are modelled to explicitly depend on the actions and characteristics of the other, including violent episodes, effectively coupling the dynamics of the two sects. We use a game theoretic framework and assume that radical factions may tune ‘strategic’ parameters to optimize given utility functions aimed at maximizing their ranks while minimizing the damage inflicted by their rivals. Constraints include limited overall resources that must be optimally allocated between indoctrination and external attacks on the other group. Various scenarios are considered, from symmetric sects whose behaviours mirror each other, to totally asymmetric ones where one sect may have a larger population or a superior resource availability. We discuss under what conditions sects preferentially employ indoctrination or violence, and how allowing sects to readjust their strategies allows for small, violent sects to grow into large, indoctrinated communities.