Cooperative games and vector-valued criteria problems

Quite often in a game there is not a strict conflict of interest among the players and they may agree to cooperate and help one another. In such cases, a solution that is Pareto-optimal is attractive since it has the property that if any other solution is used, at least one player does worse or they all do the same. The same solution concept also applies to minimization problems with several cost criteria rather than a single scalar performance index. Necessary conditions and sufficient conditions are given for Pareto-optimal solutions of static, continuous problems. Several examples are presented to illustrate the theory.