… Although the existence of equilibria is not guaranteed, we show that the market instances
arising from the Nash social welfare problem always have an equilibrium. Further, we show …

… While maximizing the Nash social welfare is NP-… additive PTAS for this problem, that is,
we give a polynomial-time algorithm that maximizes the Nash social welfare within an additive …

… In this problem, every item j has a cost of cj that will be incurred to the agent that it is allocated
to, and every agent i has a budget Bi > 0 that can be used to pay for the additive cost of the …

… Nash social welfare objective. Note this is the objective maximized by the Fisher market
equilibrium solution when the buyers have different budgets. … agents with additive valuations. We …

… The Nash social welfare (NSW) is a well-known social welfare … fairness of the NSW in a
budget-feasible allocation problem, in … are additive, our result holds with sub-additive valuation …

… of goods among agents with additive valuations. The formal … Another fairness criterion,
max Nash social welfare (NSW), ie… agents’ spending so that the resulting spending graph is a …

… additive valuations, with the goal of maximizing the geometric mean of the agents’ valuations,
ie, the Nash social welfare… be multiple spending graphs with the same Nash social welfare. …

… We study the age old problem of fair allocation of goods among agents with additive … budget
of each agent is 1, the total spending on all goods in an equilibrium is n. Also, the spending …

… additive valuations, with the goal of maximizing the geometric mean of the agents' valuations,
ie, the Nash social welfare. … allocation where the amount of spending that can go into any …

… additive valuations: budget-additive [25], separable piecewise linear concave (SPLC) [2], and
their combination, budget… and the characteristics of these ‘additive-like’ valuations, such as …