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In real life, people often participate in regional public goods games and face the social dilemma caused by the non-exclusivity of public goods. Intervening policies are expected to alleviate the social dilemma and promote intra-regional cooperation. However, owing to the existence of the costs of policy, the marginal benefits of establishing intervening policies may be diminishing, which raises questions as to whether it is necessary to establish intervening policies on a global scale; whether partial intervention is a more economical solution. In view of this, this paper investigates the evolution of cooperation in regional public goods game in the context of a central institution selecting some regions to set up an endogenous reward and punishment policy, focusing on the effects of the proportion of selection and the methods of selection on global cooperation and total social welfare. The results show that the partial intervention is superior to the whole intervention in terms of total social welfare when the coefficient of the costs of the policy is large or when strict reward and punishment are imposed and that the partial intervention can achieve the effect of the whole intervention in terms of cooperation in many cases. For all three selection methods, i.e., random selection, degree centrality selection, and size selection, size selection is optimal in most cases. Furthermore, allowing groups in non-intervened regions to spontaneously establish or abolish the policy can greatly facilitate cooperation under all three methods. Finally, we find that the central institution's prolonged and sustained intervention is essential, and its termination will lead to serious consequences. • We explore the effect of partial intervention on global cooperation and welfare. • Groups in intervened regions establish an endogenous reward and punishment policy. • The roles of the three selection methods are discussed. • Partial intervention is more profitable than whole intervention in some cases. • Prolonged and sustained intervention is necessary. [ABSTRACT FROM AUTHOR]