… the Nash social welfare when allocating a set G of indivisible goods to a set N of agents.
We study instances, in which all agents have 2-value additive valuations: The value of every …

… will assume that instances where the optimal Nash welfare is … instance admits some matching
with nonzero Nash welfare. … , 1, 2} (also known as ternary or 3-value instances) and each …

… mean of the agents’ values, known as the Nash social welfare (NSW). … to show the bounds
of 2 may be of independent interest. … Given a problem instance I and some mechanism M that …

… 2value additive valuations. Our goal is to find an allocation with maximum Nash social welfare,
ie… We give a polynomialtime algorithm to find a Nash social welfare maximizing allocation …

… 1 values only Item 1, whereas Agent 2 values this item 7.5 times more than Item … lem instance
that we considered in Example 2.2. In the unrestricted equilibrium of this instance, the price …

… Other important examples of welfare functions captured by … egalitarian social welfare, as well
as the utilitarian social welfare… Agent 1 values only Item 1, whereas Agent 2 values this item …

… We consider two cases. If i has two or more … Note that goods 1 to z have price 1/2, while
goods z + 1 through 2z have price 1/2+1/z. Suppose ALG selects agent n as the root of the tree. …

… Work An extensive work has been done on special cases of … all possible values each agent
can receive in their Nash optimal … For each vector = { 1, 2 ..., }, we check if there is an …

… from the social welfare theory [2]. The most widely used notions such as the utilitarian … of
the welfare: for instance, a simple exchange of r1 with r6 leads to a decrease of the social value …

… social welfare problem with submodular valuations. For symmetric instances, the algorithm
… finds a partial allocation that is 1 2 -EFX and preserves a large fraction of the NSW value. …