Your College Dorm and Dormmates: Fair Resource Sharing with Externalities

We study a fair resource sharing problem, where set of resources are to be shared among group agents. Each agent demands one and each can serve limited number An cares about what they get as well the externalities imposed by their mates, who share same with them. Clearly, strong notion envy-freeness, no envies another for or cannot always achieved we show that even deciding existence such strongly envy-free assignment is an intractable problem. Hence, more interesting question whether (and in situations) relaxed Pareto achieved. Under this notion, only when envy both mates other agent. In particular, interested dorm students assigned dorms capacity have dichotomous preference over dormmates. 2, exists present polynomial-time algorithm compute assignment. Nevertheless, result breaks immediately increases 3, which case envy-freeness guaranteed. addition existential results, also investigate utility guarantees (Pareto) assignments our model.