New approach to linear Stackelberg problems with multiple leaders-follower (Q2779011)

A linear static Stackelberg problem with mutiple leaders-followers is studied in this paper. The players within each group may or may not cooperate. This model extends the Stackelberg leader-follower model. An exact penalty function method, in which to the leaders objective function is added the duality gaps of the followers problem with a penalty, is developed. Because of its structure, the composite problem decomposes into a series of linear programming problems. This leads to an efficient algorithm for the composite problem. It is shown that local optimality is reached for an exact penalty function. Three examples are also presented.