A group of friends consider renting a house but they shall first agree on how to allocate its rooms and share the rent. We propose an auction mechanism for room assignment-rent division problems which mimics the market mechanism. Our auction mechanism is efficient, envy-free, individually-rational and it yields a non-negative price to each room whenever that is possible with envy-freeness.

Envy-freeness is a widely studied notion in resource allocation, capturing some aspects of fairness. The envy being inherently subjective though, it might be the case that an agent envies another agent, but from other agents' point view, she has no reason to do so. difficulty here define objectivity, since ground-truth can properly serve as basis this definition. A natural approach consider jud...

Chore division, introduced by Gardner in 1970s [10], is the problem of fairly dividing a chore among n different agents. In particular, in an envy-free chore division, we would like to divide a negatively valued heterogeneous object among a number of agents who have different valuations for different parts of the object, such that no agent envies another agent. It is the dual variant of the cel...

The article discusses the relevance of study phenomenon envy, which is due to multidimensionality this concept, since our country characterized by significant changes in moral, ethical, socio-economic and value orientations society, political, socio-cultural legal that impose their reflection both on social relations between people, but also inner world. It noted many scientists are studying ps...

We consider the fair division problem of indivisible items. It is well-known that an envy-free allocation may not exist, and a relaxed version envy-freeness, envy-freeness up to one item (EF1), has been widely considered. In EF1 allocation, agent envy others' allocated shares, but only item. many applications, we wish specify subset prioritized agents where strict needs be guaranteed from these...

Cloutier, Nyman, and Su (Mathematical Social Sciences 59 (2005), 26–37) initiated the study of envy-free cake-cutting problems involving several cakes. The classical result in this area is that when there are q players and one cake, an envy-free cake-division requiring only q − 1 cuts exists under weak and natural assumptions. Among other results, Cloutier, Nyman, and Su showed that when there ...

We conduct a computational analysis of fair and optimal partitions in additively separable hedonic games. We show that, for strict preferences, a Pareto optimal partition can be found in polynomial time while verifying whether a given partition is Pareto optimal is coNP-complete, even when preferences are symmetric and strict. Moreover, computing a partition with maximum egalitarian or utilitar...

Materialistic youth seem to be languishing while grateful youth seem to be flourishing. High school students (N = 1,035) completed measures of materialism, gratitude, academic functioning, envy, depression, life satisfaction, social integration, and absorption. Using structural equation modeling, we found that gratitude, controlling for materialism, uniquely predicts all outcomes considered: hi...

We study the fair allocation of indivisible goods among agents with identical, additive valuations but individual budget constraints. Here, goods--each a specific size and value--need to be allocated such that bundle assigned each agent is total at most agent's budget. Since envy-free allocations do not necessarily exist in context, compelling relaxations--in particular, notion envy-freeness up...