Allocating Goods on a Graph to Eliminate Envy

Abstract

We introduce a distributed negotiation framework for multi-agent resource allocation where interactions between agents are limited by a graph defining a negotiation topology. A group of agents may only contract a deal if that group is fully connected according to the negotiation topology. An impor-tant criterion for assessing the quality of an allocation of re-sources, in terms of fairness, is envy-freeness: an agent is said to envy another agent if it would prefer to swap places with that other agent. We analyse under what circumstances a se-quence of deals respecting the negotiation topology may be expected to converge to a state where no agent envies any of the agents it is directly connected to. We also analyse the computational complexity of a related decision problem, namely the problem of checking whether a given negotiation state admits any deal that would both be beneficial to every agent involved and reduce envy in the agent society.