  The indoctrination game is a complete-information contest over public
opinion. The players exert costly effort to manifest their private opinions in
public in order to control the discussion, so that the governing opinion is
similar to theirs. Our analysis provides a theoretical foundation for the
silent majority and vocal minority phenomena, i.e., we show that all moderate
opinions remain mute in equilibrium while allowing extremists full control of
the discussion. Moreover, we prove that elevated exposure to others' opinions
increases the observed polarization among individuals. Using these results, we
formulate a new social-learning framework, referred to as an indoctrination
process.
