In non-cooperative two-person games Nash equilibria can be dominated. When a third player — the regulator — can influence the cost structure of the game, it is sometimes possible to reduce the degree of dominance of the non-cooperative equilibrium. We formulate the regulator's problem as minimization of a (properly chosen) distance between the Nash equilibrium point(s) and a desired point of the Pareto frontier. We are interested in characterizing cases where — and offer conditions under which — regulation can be effective. Effectiveness demands to elicit cooperation while ensuring the regulated cooperative outcome of the game to be non-dominated by the non-regulated one.