A group game of multiple attribute decision making

Multiple Attribute Decision Making (MADM) problem is a management science technique, which is popularly used to rank the priority of alternatives with respect to their competing attributes. It is popularly used in diverse fields such as engineering management, portfolio selection, transportation planning, and performance evaluation. Weights form the core of MADM: it is obvious that different weights lead to various evaluation results and decisions. Several approaches have been developed for assessing the weights of MADM problems, e.g., the eigenvector method, ELECTRE, and TOPSIS. However, an assessment approach of weights in MADM, which meets both the need of simplicity interface for practitioners and concrete theory for scholars is not easy, and balancing these two aspects is a challenging and tough task. Since the pay-off matrix in game theory could be regarded as a simple interface for data input/output, and very few scholars had ever explored the two-person zero-sum game on MADM problems. In this paper, the weights of a MADM problem are obtained by formulating it as a two-person zero-sum game with multiple decision makers. The group equilibrium solution, i.e., consensus of weights and the resolution steps for such a group MADM game has also been originally developed and validated in this study. Finally, an actual case of selecting the appropriate portfolio decision for a paper company is illustrated.