A Sensitivity Based Approach to Determining Non-Cooperative Solutions in Nash and Stackelberg Games

Abstract

A sensitivity based approach is presented to determine Nash solution(s) in multiobjective problems modeled as a non-cooperative game. The proposed approach provides an approximation to the rational reaction set (RRS) for each player. An intersection of these sets yields the Nash solution for the game. An alternate approach for generating the RRS based on design of experiments (DOE) combined with response surface methodology (RSM) is also explored. The two approaches for generating RRS are compared on three example problems to find Nash and Stackelberg solutions. It is seen that the proposed sensitivity based approach (i) requires less computational effort than a RSM-DOE approach, (ii) is less prone to numerical errors than the RSM-DOE approach, (iii) is able to find all Nash solutions when the Nash solution is not a singleton, (iv) is able to approximate non linear RRS, and (v) is able to find better a Nash solution on an example problem than the one reported in the literature.