Peer effects and local congestion in networks

We study linear quadratic games played on a network. Agents face peer effects with distance-one neighbors, and strategic substitution with distance-two neighbors (local congestion). For this class of games, we show that an interior equilibrium exists both in the high and in the low regions of the largest eigenvalue, but may not exist in the intermediate region. In the low region, equilibrium is proportional to a weighted version of Bonacich centrality, where weights are themselves centrality measures for the network. Local congestion has the effect of decreasing equilibrium behavior, potentially affecting the ranking of equilibrium actions. When strategic interaction extends beyond distance-two, equilibrium is characterized by a “nested” Bonacich centrality measure, and existence properties depend on the sign of strategic interaction at the furthest distance. We support the assumption of local congestion by presenting empirical evidence from a secondary school Dutch dataset.