… the problem of maximizing the Nash social welfare (NSW). In … is closely related to the Fisher
market model: if we relax the … correspond to market equilibria for the linear Fisher market. …

… We study linear Fisher markets with satiation. In these … We study Fisher markets with
linear valuations and earning and utility limits. In markets with utility limits, a market equilibrium …

… Fisher market, a fundamental model of an economy, whose benchmark is precisely the (weighted)
Nash social welfare… perfect substitutes, the Fisher market mechanism yields a constant …

… the Fisher market equilibrium, we formulate the Fisher market … is a necessary condition for
the Nash equilibria (NE) and … There may exist NESPs, whose social welfare (ie, sum of the …

… We show that the Fisher market game always has a pure Nash equilibrium, for buyers with …
fying the social welfare loss due to the strategic behavior of buyers in the Fisher market game. …

… an exact solution (ie, a Nash optimal allocation) can be found … algorithms for optimizing Nash
social welfare under concave … equilibria of Fisher markets or using real stable polynomials. …

… We define a modified Fisher market instance (N,M,V,e ) using the same set of agents, goods
and agent valuations, but with different budgets. For each agent i, we set their new budget …

… We define a modified Fisher market instance (N,M,V,e ) using the same set of agents, goods
… It follows that A and prices p are market equilibrium for the Fisher market instance (N,M,V,e )…

… relaxing the problem to a class of Fisher markets and then rounding an equilibrium allocation
to an … earning limits into the resulting Fisher market. For additive valuations, this creates a …

… The following theorem, which we believe is of independent interest, states that in Fisher
markets with Leontief utilities, approximate market equilibria are close to exact equilibria in terms …