We focus on multi-agent, multi-objective problems, particularly on those where the objectives admit a potential structure. We show that the solution to the potential multi-objective problem is always a noncooperative optimum for the multi-agent setting. Furthermore, we identify a class of problems for which every noncooperative solution can be computed via the potential problem. We also establish a class of problems in which the solution to the potential problem yields a solution to the cooperative multi-agent problem, and a further subclass where the solution to the potential problem simultaneously represents both a cooperative and a noncooperative solution, under aligned player objective preferences.
We apply this framework to multi-portfolio problems and demonstrate that Portfolio Return, Portfolio Variance, Transaction Costs, and Sustainability Score can be handled in different ways to obtain models fitting all the problem classes we identify.