Stochastic bi level programming with multi-choice for Stackelberg game via fuzzy programming

In this paper, we study Stackelberg game as a multi‐choice stochastic bi‐level programming problem. In Stackelberg game, we have introduced the concept of leader at the higher level and the followers at lower level of the problem. We have considered the parameters of the constraints follow normal distribution and the cost coefficients of the objective functions are multi‐choice types. To solve the problem, at first all the probabilistic constraints are transformed into deterministic constraints. Further, a general transformation technique with the help of binary variables is used to transform the multi‐choice type cost coefficients of the objective functions of decision makers (DMs). Then the transformed problem is considered as a deterministic bi‐level programming problem. Finally, a case study is presented to illustrate the usefulness of the paper.