Final answer:
According to Wallerstein's world systems theory, core nations exploit peripheral nations for resources, maintaining economic dominance and perpetuating global inequality.
Step-by-step explanation:
In Wallerstein’s world systems theory, core nations are dominant capitalist countries that are characterized by a high level of industrialization, technology, and urban development. According to the theory, these nations exploit peripheral nations for resources, which places them in a position of economic dependence. An example of how core nations maintain their dominant positions is through mechanisms like the North American Free Trade Agreement (NAFTA) where core countries, such as the United States, can exert influence and control to gain beneficial positions in global trade. Hence, Option 1: Exploit peripheral nations for resources would be the correct answer to the question regarding core nations' actions in Wallerstein’s theory.