Efficient networks in games with local complementarities

We address the problem of a planner looking for the efficient network when agents play a network game with local complementarities and links are costly. We show that for general network cost functions, efficient networks belong to the class of Nested-Split Graphs. Next, we refine our results and find that, depending on the specification of the network cost function, complete networks, core-periphery networks, dominant group architectures, quasi-star and quasi-complete networks can be efficient.