Conflict parties are frequently involved into more than one conflict at a given time. In this paper the interrelated structure of conflictive relations is modeled as a conflict network where opponents are embedded in a local structure of bilateral conflicts. Conflict parties invest in specific conflict technology to attack their respective rivals and defend their own resources. We show that there exists a unique equilibrium for this conflict game and examine the relation between aggregated equilibrium investment (interpreted as conflict intensity) and underlying network characteristics. The derived results have implications for peaceful resolutions of conflicts because neglecting the fact that opponents are embedded into an interrelated conflict structure might have adverse consequences for conflict intensity.