Nash Social Welfare in Multiagent Resource Allocation

We study different aspects of the multiagent resource allocation problem when the objective is to find an allocation that maximizes Nash social welfare, the product of the utilities of the individual agents. The Nash solution is an important welfare criterion that combines efficiency and fairness considerations. We show that the problem of finding an optimal outcome is NP-hard for a number of different languages for representing agent preferences; we establish new results regarding convergence to Nash-optimal outcomes in a distributed negotiation framework; and we design and test algorithms similar to those applied in combinatorial auctions for computing such an outcome directly

Reallocation Problems in Agent Societies: A Local Mechanism to Maximize Social Welfare

Resource reallocation problems are common in real life and therefore gain an increasing interest in Computer Science and Economics. Such problems consider agents living in a society and negotiating their resources with each other in order to improve the welfare of the population. In many studies however, the unrealistic context considered, where agents have a flawless knowledge and unlimited interaction abilities, impedes the application of these techniques in real life problematics. In this paper, we study how agents should behave in order to maximize the welfare of the society. We propose a multi-agent method based on autonomous agents endowed with a local knowledge and local interactions. Our approach features a more realistic environment based on social networks, inside which we provide the behavior for the agents and the negotiation settings required for them to lead the negotiation processes towards socially optimal allocations. We prove that bilateral transactions of restricted cardinality are sufficient in practice to converge towards an optimal solution for different social objectives. An experimental study supports our claims and highlights the impact of a realistic environment on the efficiency of the techniques utilized.Resource Allocation, Negotiation, Social Welfare, Agent Society, Behavior, Emergence

Approximating the {Nash} Social Welfare with Budget-Additive Valuations

We present the first constant-factor approximation algorithm for maximizing the Nash social welfare when allocating indivisible items to agents with budget-additive valuation functions. Budget-additive valuations represent an important class of submodular functions. They have attracted a lot of research interest in recent years due to many interesting applications. For every $\varepsilon > 0$, our algorithm obtains a $(2.404 + \varepsilon)$-approximation in time polynomial in the input size and $1/\varepsilon$. Our algorithm relies on rounding an approximate equilibrium in a linear Fisher market where sellers have earning limits (upper bounds on the amount of money they want to earn) and buyers have utility limits (upper bounds on the amount of utility they want to achieve). In contrast to markets with either earning or utility limits, these markets have not been studied before. They turn out to have fundamentally different properties. 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 that the set of equilibria is not convex, answering a question of [Cole et al, EC 2017]. We design an FPTAS to compute an approximate equilibrium, a result that may be of independent interest