Beziehungen spielen lassen — to let one’s connections play, to use contacts to get something
Beziehungen schaden nur dem, der sie nicht hat. — Connections only harm the person who does not have them. The saying is meant ironically.
die Vetternwirtschaft — the cousins’ economy, nepotism
die Spezlwirtschaft — the buddies’ economy, from the Bavarian Spezl, a buddy