Bilevel direct search method for leader-follower problems and application in health insurance

In the paper, we propose a bilevel direct search method for the distributed computation of equilibria in leader-follower problems. This type of direct search methods is designed for characterizing the decision making process where the players' objective functions are not analytically available. We investigate the convergence of the accumulation points yielded by the method to the stationary points of the problems. Finally, we apply the method to a health insurance problem and carry out several numerical examples to illustrate how the method performs when solving leader-follower problems.