A Word for a Society in which the Power Source is Your Contacts

Solution 1:

Following on from cronyism, you can extend it to:

Crony Capitalism is a term describing an economy in which success in business depends on close relationships between business people and government officials.

Crony capitalism is believed to arise when business cronyism and related self-serving behavior by businesses or businesspeople spills over into politics and government, or when self-serving friendships and family ties between businessmen and the government influence the economy and society to the extent that it corrupts public-serving economic and political ideals.

Solution 2:

Connection is the key word to refer to a non-meritocratic society.

• A person, especially one of influence or importance, with whom one is associated, as by kinship or common interests: used her connections to land a job. .(AHD)

• I am living in a world where connections are more important than meritocracy

Cronyism , as suggested in a comment, is a useful term, but it is mainly used in political, public contexts:

• (Government, Politics & Diplomacy) the practice of appointing friends to high-level, esp political, posts regardless of their suitability. (Collins)

Solution 3:

Collusion, or a secret or illegal cooperation or conspiracy, especially in order to cheat or deceive others, could fit the bill (ie "I am [operating] in a state of collusion."). I'd imagine your best bet will end up being a phrase rather than a single word.