The Unreasonable Fairness of Maximum Nash Welfare

The maximum Nash welfare (MNW) solution --- which selects an allocation that maximizes the product of utilities --- is known to provide outstanding fairness guarantees when allocating divisible goods. And while it seems to lose its luster when applied to indivisible goods, we show that, in fact, the MNW solution is unexpectedly, strikingly fair even in that setting. In particular, we prove that it selects allocations that are envy free up to one good --- a compelling notion that is quite elusive when coupled with economic efficiency. We also establish that the MNW solution provides a good approximation to another popular (yet possibly infeasible) fairness property, the maximin share guarantee, in theory and --- even more so --- in practice. While finding the MNW solution is computationally hard, we develop a nontrivial implementation, and demonstrate that it scales well on real data. These results lead us to believe that MNW is the ultimate solution for allocating indivisible goods, and underlie its deployment on a popular fair division website

Negotiation Strategy of Divisible Tasks for Large Dataset Processing

International audienceMapReduce is a design pattern for processing large datasets on a cluster. Its performances depend on some data skews and on the runtime environment. In order to tackle these problems, we propose an adaptive multiagent system. The agents interact during the data processing and the dynamic task allocation is the outcome of negotiations. These negotiations aim at improving the workload partition among the nodes within a cluster and so decrease the runtime of the whole process. Moreover, since the negotiations are iterative the system is responsive in case of node performance variations. In this paper, we show how, when a task is divisible, an agent may split it in order to negotiate its subtasks

Network topology and the behaviour of socially-embedded financial markets

We study the impact of the network topology on various market parameters (volatility, liquidity and efficiency) when three populations or artificial trades interact (Noise, Informed and Social Traders). We show, using an agent-based set of simulations that choosing a Regular, a Erdös-Rényi or a scale free network and locating on each vertex one Noise, Informed or Social Trader, substantially modifies the dynamics of the market. The overall level of volatility, the liquidity and the resulting efficiency are impacted by this initial choice in various ways which also depends upon the proportion of Informed vs. Noise Traders