In this paper we study a model of weighted network formation. The bilateral interaction is modeled as a Tullock contest game with the possibility of a draw. We describe stable networks under different concepts of stability. We show that a Nash stable network is either the empty network or the complete network. The complete network is not immune to bilateral deviations. When we allow for limited farsightedness, stable networks immune to bilateral deviations must be complete $M$-partite networks, with partitions of different sizes. The empty network is the efficient network. We provide several comparative statics results illustrating the importance of network structure in mediating the effects of shocks and interventions. In particular, we show that an increase in the likelihood of a draw has a non-monotonic effect on the level of wasteful contest spending in the society. To the best of our knowledge, this paper is the first attempt to model weighted network formation when the actions of individuals are neither strategic complements nor strategic substitutes.