<p>We study the implementability of quota policies in assignment games with constraints, where the planner can set a quota system before the allocation of resources. The distributional constraint specifies demand floors for subgroups of agents. In addition, the planner contends with a group influence constraint, where a larger group of agents exercises more significant influence on a quota policy. We completely characterize the set of all implementable quota systems and provide a game-theoretic interpretation for the implementability condition. We also characterize the extreme points of the polytope defined by the implementable demand floor quotas, and study optimal demand floors in a class of two-stage quota-setting games.</p>