Envy-Free Allocations Respecting Social Networks through Information Witholding

Fair division is one of the main problems in computational social choice. Recently, there was a line of work that introduce social networks in the classic notion of envy-freeness and proportionality. Another line of work considered approximations of these classic notions, as such allocations might not exist in general. To address the limitations of both approaches we propose a novel fairness notion that combines social networks and the idea of hiding items. Considering social network allows achieving a lower number of hidings in the worst case. In this work, we also study the computational complexity of such allocations from a parameterized perspective. We consider some well-studied graph parameters such as treewidth, cliquewidth, and other parameters such as the number of item types and number of agent types. We identified cases when these problem becomes tractable and cases when these problem is W[1]-hard or above. Keywords: Fair division, parameterized algorithms, W[1]-hardness, treewidth, cliquewidth, exact algorithms.