Nash Welfare Allocation Problems: Concrete Issues

The allocation of m resources between n agents is an AI problem with a great practical interest for automated trading. The general question is how to configure the behavior of bargaining agents to induce a socially optimal allocation. The literature contains many proposals for calculating a social welfare but the Nash welfare seems to be the one which has the most interesting properties for a fair agent society. It guarantees that all resources are fairly distributed among agents respecting their own preferences. This article shows first that the computation of this welfare is a difficult problem, contrary to common intuition. Many counter-examples describe the pitfalls of this resolution. In a second step, we describe our distributed multi-agent solution based on a specific agent’sbehavior and the results we get on difficult instances. We finally claim that this anytime solution is the only one able to effectively address this problem of obvious practical interest.