Final answer:
Indigenous societies with 'big man' leaders existed in Melanesia and New Guinea, where leaders gained prominence through wealth accumulation and acts of public generosity without formal coercive power.
Step-by-step explanation:
Indigenous tribal level societies with leaders called "big men" were typically found in Melanesia and New Guinea. These societies, such as the Kapauku of New Guinea, were generally egalitarian, but a man could rise to prominence through accumulating wealth, public acts of generosity, such as sponsoring feasts, and helping young men pay bride wealth. Additionally, they had the ability to settle disputes and represent their communities in negotiations with outsiders. Big man leadership, unlike centralized societies with formal authority figures like chiefs or kings, relied on persuasive power rather than coercive authority.