This paper studies the allocation of a fixed number of an indivisible and homo-

geneous commodity among a set of agents. Each agent possesses a weak preference

relation over the set of feasible assignments they can receive. Unlike classical

models, we examine settings where agents hold asymmetric institutional power,

allowing dissatisfied coalitions to challenge or reject a proposed allocation. In this

framework, we introduce a concept of stability that generalizes Pareto optimality

and ensures conflict avoidance. We establish necessary and sufficient conditions

for the existence of stable allocations independently of agents’ preferences, and

characterize them when agent preferences are single-peaked or single-dipped.

Key words: Allocation problem, stability, blocking coalitions, single-peaked

preferences, single-dipped preferences.