Using a laboratory experiment, we behaviourally study the impact of a sudden increase in the common-pool size on within-group conflict, i.e., the paradox of the plenty. We also consider the potential role of governance in avoiding this paradox. In the first stage, a randomly-chosen leader of the group determines how much of the common-pool resource to protect from second-stage conflict. In the next stage, each group member allocates his private endowment between working or fighting for a share of the unprotected resource. We consider two treatments: anarchy (consisting of the second stage only) and with a leader deciding in the first stage. We find that the existence of institutions is not always better than anarchy. This is aggravated when the resource size is higher. Group conflict (income) decreases (increases) only when leaders chose the strongest resource protection. When leaders are malevolent, i.e., they chose weak resource protection, outcomes are worse than when institutions are absent.