We model an infinitely repeated Tullock contest, over the sharing of some given resource, between two ethnic groups. The resource is allocated by a composite state institution according to relative ethnic control; hence the ethnic groups contest the extent of institutional ethnic bias. The contest yields the per-period relative influence over institutions, which partly spills over into the next period, by affecting relative conflict efficiency. Our model generates non-monotone evolution of both conflict and distribution. Results suggest that external interventions, when effective in reducing current conflict and protecting weaker groups, may end up sowing the seeds of greater future conflict.