A Nash equilibrium based decision-making method for performance evaluation: a case study

In organizational management, selecting the most appropriate combination of balanced scorecard (BSC) indicators as an equilibrium point based on scientific methods is of great value. In this paper, a new approach based on the balanced scorecard and game theory has been developed for evaluating the performance of an Iranian company to determine the most appropriate combination of BSC indicators and to build an equilibrium point between financial and non-financial performance measures. The organization’s strategic objectives have been translated into a set of performance measures distributed among four perspectives of financial, customer, internal business processes, and learning and growth. Considering each perspective of BSC as a player in a four-person cooperative game, a bi-objective mathematical model of a finite-discrete game in normal form, based on the Nash solution, is proposed to specify the relationship among indicators in the strategy map, to determine the equilibrium points in the BSC, and to control the organizational costs. The results suggest that the proposed model successfully determines the best combination of indicators, and an equilibrium point in the BSC to minimize the costs and maximize perspectives’ payoff of the BSC without undertaking complicated mathematical computation. Adoption of four indicators of generating new R&D activities, consistency of the working team, growing satisfaction of existing customers, and potential growth in operating income by four players was suggested as the best combination of BSC indicators as an equilibrium point. The proposed model was validated using the Taguchi method to prove that it has been accurate and reliable.