Multiagent Fair Optimization with Lorenz Dominance

This paper deals with fair optimization problems where several agents are involved. In this setting, a solution is evaluated by a vector whose components are the utility of the agents for this solution, and one looks for solutions that fairly satisfy all the agents. Lorenz dominance has been proposed in economics to refine the Pareto dominance by taking into account satisfaction inequality among the agents. The computation of Lorenz efficient solutions in multiagent optimization is however challenging (it has been shown intractable and NP-hard on certain problems). Nevertheless, to our knowledge, very few works address this problem. We propose thus in this work new methods to generate Lorenz efficient solutions. More precisely, we consider the adaptation of the well-known two-phase method proposed in biobjective optimization to the bi-agent optimization case, where one wants to directly compute the Lorenz efficient solutions. We study the efficiency of our method by applying it on the bi-agent knapsack problem.