Solution concepts based on security levels in constrained multicriteria convex games

In this paper, the concept of Pareto-Optimal Security Strategies defined for multicriteria zero-sum matrix games is extended to games with continuous kernel. This extension replaces the notion of Pareto efficiency by the proper Pareto efficiency avoiding the undesirable properties concerning the ratio of the rate of gain in one criterion over the corresponding rate of loss in another criterion. Methods for obtaining strategies that yield Pareto and proper Pareto security levels to the players are presented. A scalar game is derived and it is proved that to be solution of the new game with strictly positive scalarization is a necessary and sufficient condition for a strategy to be a Proper Pareto-Optimal Security Strategy.