The indoctrination game is a full-information contest over public opinion. The players exert costly effort to publicly express their private opinions, striving to dominate the discourse and thereby steer the prevailing opinion to  align with their own. Our research provides a theoretical basis for the phenomena of the silent majority and vocal minority. We demonstrate that, in equilibrium, moderate opinions are suppressed, thereby affording extremists unbridled control over the dialogue. Furthermore, we show that heightened exposure to diverse perspectives escalates the perceptible polarization within a given population.  Drawing on these insights, we formulate a new social-learning framework, referred to as  'an indoctrination process'. Consistent with empirical evidence, our findings forecast a monotonic escalation in polarization as societal interconnectedness intensifies.