Allocating Goods on a Graph to Eliminate Envy
Yann Chevaleyre, Ulle Endriss, Nicolas Maudet

Abstract:
We introduce a distributed negotiation framework for multiagent
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 important criterion for assessing the quality
of an allocation of resources, 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
sequence 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.