Cooperation, Competition and Entry in a Tullock Contest

We propose a model of network formation in a Tullock contest. Agents first form their partnerships and then choose their investment in the contest. While a link improves the strength of an agent, it also improves the position of her rival. It is thus not obvious that they decide to cooperate. We characterize all pairwise equilibrium networks and find that the network formation process can act as a barrier to entry to the contest. We then analyze the impact of network formation on total surplus and find that a social planner can increase total surplus by creating more asymmetry between agents, as long as this does not reduce the number of participating agents. We show that barriers to entry may either hurt total surplus, as the winner of the prize does not exploit all the possible network benefits, or improve total surplus since less rent is dissipated when competition becomes less fierce. Finally, when networking acts as an endogenous barrier to entry, no pairwise equilibrium network is efficient.