Multi-objective potential games via hypervolume maximization

Multi-objective games model strategic interactions where multiple agents simultaneously optimize different conflicting objectives in a noncooperative setting. Pareto Equilibria have been introduced as a fundamental solution concept, ensuring that no player can unilaterally improve on one objective without worsening at least another. While the existence of such equilibria has been well established, selecting a specific, desirable solution remains a nontrivial task. We focus on multi-objective games where each objective admits a corresponding weighted potential function. We also address the corresponding centralized potential problem of optimizing the multiple potential functions simultaneously. Although potential structures have been explored also in the multi-objective context, the problem of efficiently selecting a Pareto solution remains largely unresolved. We focus on the Hypervolume Maximization scalarization method both for each agent’s and for the potential problem, which maximizes the improvement of the objectives with respect to a given reference point. We analyze how solving the potential problem through this technique results in computing solutions to the original multi-objective game.