Envy-Free Allocations Respecting Social Networks
Robert Bredereck, Andrzej Kaczmarczyk, and Rolf Niedermeier

TL;DR
This paper introduces a social network-aware variant of envy-freeness in resource allocation, analyzing its computational complexity and identifying cases where it is easier or harder to find envy-free allocations.
Contribution
It formalizes a new local envy-freeness concept based on social networks and studies its computational complexity, including fixed-parameter tractability results.
Findings
Certain cases become polynomial-time solvable under social network constraints.
Some problems are harder or easier compared to classical envy-freeness depending on preferences and network structure.
A connection to a directed, colored subgraph isomorphism problem is established.
Abstract
Finding an envy-free allocation of indivisible resources to agents is a central task in many multiagent systems. Often, non-trivial envy-free allocations do not exist, and, when they do, finding them can be computationally hard. Classical envy-freeness requires that every agent likes the resources allocated to it at least as much as the resources allocated to any other agent. In many situations this assumption can be relaxed since agents often do not even know each other. We enrich the envy-freeness concept by taking into account (directed) social networks of the agents. Thus, we require that every agent likes its own allocation at least as much as those of all its (out)neighbors. This leads to a "more local" concept of envy-freeness. We also consider a "strong" variant where every agent must like its own allocation more than those of all its (out)neighbors. We analyze the classical…
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