Weak stackelberg problem and mixed solutions under data perturbations11this paper is based upon a communication presented at the 14th symposium on mathematical programming with data perturbation, Washington D.C. 1992. This research has been supported by M.U.R.S.T Roma, Italia.$ef:

Abstract

A two-level optimization problem corresponding to a Stackelberg game in which one of the two players has the leadership in playing the game is considered. First, a review of previous results about existence and stability of solutions and approximate solutions is presented in the case in which the solutions set to the lower level problem is a singleton, as well as in the case in which the response function of the follower is multi-valued. Then, when some like convexity assumption on the lower level problem is not satisfied, different mixed extensions of the problem are considered and existence and stability of e-mixed solutions introduced by the authors are investigated with respect to perturbations on the data