The Game Theory Approach for Solving the Hierarchical and Decentralized Bi-Level Problem

Abstract

This paper presents a game theory approach to solve two types op problem, hierarchical and decentralized bi-level multi-objective problem with multiple objective functions at the upper level and multiple players at the lower level. The sensitivity based approach is applied for numerical approach. A sensitivity based algorithm is proposed to the Hierarchical and decentralized bi-level multi-objective problem. Two scenarios are studied in this paper for modeling the decentralized bi-level multi-objective problem. The first scenario considers the cooperative game as interaction between the players at upper level and the lower level individually. The interaction between the upper and lower level is considered as Stackelberg. On the second scenario, the interaction in the lower level is modeled by Nash game. The sensitivity based method has been used to provide an approximation to the rational reaction set (RRS) for each player. An alternate approach for generating the RRS based on design of experiments (DOE) combined with response surface methodology (RSM) is also explored. Two numerical examples are given to demonstrate the proposed algorithm for the both scenario. It is seen that the proposed sensitivity based approach is able to approximate non linear RRS. For the hierarchical approach, one numerical example is studied to show the application of the algorithm.