Connecting friends

We study how people form networks through introductions. We consider a model where players with different ability levels are connected in a network. The players seek to match with someone they are linked to in the network (i.e., their neighbors), and they prefer high-ability neighbors over low-ability ones. We investigate whether a player will strategically introduce two unacquainted neighbors to each other to improve her own matching outcome. We find that this is possible if (i) the player making the introduction is less capable than both of the neighbors she considers introducing, and (ii) there exists an even-length alternating path—a sequence of linked players that alternate between matching and not matching with the next player on the sequence—from one of the neighbors to the introducer. The characterization based on alternating paths arises because an introduction can trigger a chain of rematches along these paths. Then, we characterize stable networks and efficient networks, and we show that stability and efficiency do not imply each other. Finally, we consider several extensions, such as alternative matching processes and incomplete information.