Fair Division of Indivisible Goods

In this paper, we study the problem of allocating indivisible goods among agents in a fair way. Envy-freeness and Pareto optimality have been used extensively to assess the fairness of allocation. Since envy-free allocations are not guaranteed to exist for indivisible goods. We utilize a relaxed version of envy-freeness called envy-freeness up to one less preferred good (EFL) which states that an allocation is fair if no agent prefers another agent’s bundle after removing an item from the other agent’s bundle that is valued less than the agent’s bundle or the other agent’s bundle has at most one good that is positively valued by the agent. We establish the existence of allocations that satisfies EFL in conjunction with Pareto optimality under additive valuations by providing a polynomial time algorithm. Moreover, we study Nash welfare associated with the algorithm and empirically demonstrate higher values when compared to the existing approximation of maximum Nash welfare solution over a large set of randomly generated instances.