Determining the Best Combination of Perspective indicators of Balanced Scorecard by using Game Theory

Document Type : Original Manuscript


1 Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

2 Department of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, Iran

3 Department of Industrial Engineering, Golpayegan University of Technology, Golpayegan, Iran


Manufacturing performance measurement offers an appropriate program for future planning, controlling, and decision-making of organizations as well as determination of their present status. This paper aimed to assess a firm’s manufacturing performance using a reasonably comprehensive integrated BSC- Game model to empirically determine the importance of the perspectives and indicators under evaluation and the best combination of indicators A mathematical model was employed to determine the equilibrium among the four perspectives of the balanced scorecard (BSC) as four players in a cooperative game to specify the relationship among indicators in the strategy map of Esfahan Steel Complex Company. The GAMS optimization package was used to solve the model. The results suggest that the decision-makers of Esfahan Steel Company consider innovation, modern technologies, customer satisfaction, and equity profitability as the best combination of strategies and equilibrium point in the BSC. In fact, the proposed mathematical model successfully provided an equilibrium to minimize the costs and maximize the perspectives’ payoff of the BSC. The main contribution of this paper lies to the adaption of a game theory approach to performance measurement in the industrial sector that makes balancing in the BSC become more real

Graphical Abstract

Determining the Best Combination of Perspective indicators of Balanced Scorecard by using Game Theory


  • Proposing a new approach based on the balanced scorecard (BSC) and game theory.
  • Proposing a bi-objective mathematical model, based on Nash solution for a four-player game to specify the relationship among indicators in the strategy map.
  • Using the proposed model to determine the equilibrium point in the BSC, and to control the organizational costs.


Ahmadi‐Javid, A. and Hoseinpour, P. (2018) “Cooperative advertising in a capacitated manufacturer–retailer supply chain: a game‐theoretic approach,” International Transactions in Operational Research. Wiley Online Library, 25(5), pp. 1677–1694.
Akkermans, H. and Van Oorschot, K. (2002) “Developing a balanced scorecard with system dynamics,” Journal of the operational research society, 40(56), pp. 931–941.
Aliakbari Nouri, F., Shafiei Nikabadi, M. and Olfat, L. (2019) “Developing the framework of sustainable service supply chain balanced scorecard (SSSC BSC),” International Journal of Productivity and Performance Management. Emerald Publishing Limited, 68(1), pp. 148–170.
Alinezhad, A. et al. (2010) “Evaluation of effectiveness of implementing quality management system (ISO9001: 2000) Using BSC Approach in NIGC,” Journal of Optimization in Industrial Engineering. QIAU, (6), pp. 33–42.
Barari, S. et al. (2012) “A decision framework for the analysis of green supply chain contracts: An evolutionary game approach,” Expert systems with applications. Elsevier, 39(3), pp. 2965–2976.
Bénet, N., Deville, A. and Naro, G. (2019) “BSC inside a strategic management control package,” Journal of Applied Accounting Research. Emerald Publishing Limited, 20(1), pp. 120–132.
Brewer, P. C. and Speh, T. W. (2001) “Adapting the balanced scorecard to supply chain management.,” SUPPLY CHAIN MANAGEMENT REVIEW, V. 5, NO. 2 (MAR./APR. 2001), P. 48-56: ILL.
Cebeci, U. (2009) “Fuzzy AHP-based decision support system for selecting ERP systems in textile industry by using balanced scorecard,” Expert Systems with Applications. Elsevier, 36(5), pp. 8900–8909.
Chakrabarty, D. et al. (2008) “Efficiency, Fairness and Competitiveness in Nash Bargaining Games,” in International Workshop on Internet and Network Economics. Springer, pp. 498–505.
Chavoshlou, A. S., Khamseh, A. A. and Naderi, B. (2019) “An optimization model of three-player payoff based on fuzzy game theory in green supply chain,” Computers & Industrial Engineering. Elsevier, 128, pp. 782–794.
Chou, S.-Y., Chang, Y.-H. and Shen, C.-Y. (2008) “A fuzzy simple additive weighting system under group decision-making for facility location selection with objective/subjective attributes,” European Journal of Operational Research. Elsevier, 189(1), pp. 132–145.
Chytas, P., Glykas, M. and Valiris, G. (2011) “A proactive balanced scorecard,” International Journal of Information Management. Elsevier, 31(5), pp. 460–468.
Dincer, H., Yüksel, S. and Martinez, L. (2019) “Balanced scorecard-based Analysis about European Energy Investment Policies: A hybrid hesitant fuzzy decision-making approach with Quality Function Deployment,” Expert Systems with Applications. Elsevier, 115, pp. 152–171.
Dominici, G. (2011) “Game theory as a marketing tool: uses and limitations,” Gandolfo Dominici/Elixir Marketing, 36, pp. 3524–3528.
Eskafi, S., Roghanian, E. and Jafari-Eskandari, M. (2015) “Designing a performance measurement system for supply chain using balanced scorecard, path analysis, cooperative game theory and evolutionary game theory: A Case Study,” International Journal of Industrial Engineering Computations, 6(2), pp. 157–172.
Froschauer, J. et al. (2012) “A serious heritage game for art history: Design and evaluation of ThIATRO,” in 2012 18th International Conference on Virtual Systems and Multimedia. IEEE, pp. 283–290.
Goldman, J. E. and Ahuja, S. (2009) “Integration of COBIT, balanced scorecard & SSE-CMM as a strategic information security management (ISM) framework,” in Proceedings of the 10th Annual Information Security Symposium. CERIAS-Purdue University, p. 19.
Gumbus, A. (2005) “Introducing the balanced scorecard: creating metrics to measure performance,” Journal of management education. Sage Publications Sage CA: Thousand Oaks, CA, 29(4), pp. 617–630.
Harsanyi, J. (1959) “C.,(1959), A bargaining model for the cooperative n-person games,” Contributions to the theory of Games IV. Princeton University Press, Princeton, pp. 325–355.
Hamamura, J. (2019) “Unobservable transfer price exceeds marginal cost when the manager is evaluated using a balanced scorecard,” Advances in accounting. Elsevier, 44, pp. 22–28.
Ten Have, S. et al. (2003) Key management models: The management tools and practices that will improve your business. Pearson Education.
Hernández, E., Barrientos, A. and Del Cerro, J. (2014) “Selective Smooth Fictitious Play: An approach based on game theory for patrolling infrastructures with a multi-robot system,” Expert Systems with Applications. Elsevier, 41(6), pp. 2897–2913.
Hoque, Z., Barnabè, F. and Busco, C. (2012) “The causal relationships between performance drivers and outcomes,” Journal of Accounting & Organizational Change. Emerald Group Publishing Limited.
Huang, H.-C. (2009) “Designing a knowledge-based system for strategic planning: A balanced scorecard perspective,” Expert Systems with Applications. Elsevier, 36(1), pp. 209–218.
Jami Pour, M. et al. (2017) “Developing a new framework for evaluating e-learning systems: integrating BSC and FAHP,” Kybernetes. Emerald Publishing Limited, 46(8), pp. 1303–1324.
Kajtazi, M. and Holmberg, N. (2019) “IS Education Revisited: Reflections on a BSc Program in Business Information Systems Design,” in 2019 5th International Conference on Information Management (ICIM). IEEE, pp. 144–149.
Kalender, Z. T. and Vayvay, Ö. (2016) “The fifth pillar of the balanced scorecard: Sustainability,” Procedia-Social and Behavioral Sciences. Elsevier, 235, pp. 76–83.
Kaplan, R. S. and Norton, D. P. (1996) “Strategic learning & the balanced scorecard,” Strategy & Leadership. MCB UP Ltd, 24(5), pp. 18–24.
Keyes, C. L. M. (2005) “Mental illness and/or mental health? Investigating axioms of the complete state model of health.,” Journal of consulting and clinical psychology. American Psychological Association, 73(3), p. 539.
Lee, A. H. I., Chen, W.-C. and Chang, C.-J. (2008) “A fuzzy AHP and BSC approach for evaluating performance of IT department in the manufacturing industry in Taiwan,” Expert systems with applications. Elsevier, 34(1), pp. 96–107.
Li, X., Gu, X. J. and Liu, Z. G. (2009) “A strategic performance measurement system for firms across supply and demand chains on the analogy of ecological succession,” Ecological Economics. Elsevier, 68(12), pp. 2918–2929.
Mendoza-Alonzo, J., Zayas-Castro, J. and Charkhgard, H. (2019) “Office-based and home-care for older adults in primary care: A comparative analysis using the Nash bargaining solution,” Socio-Economic Planning Sciences. Elsevier.
Modak, M., Ghosh, K. K. and Pathak, K. (2018) “A BSC-ANP approach to organizational outsourcing decision support-A case study,” Journal of Business Research. Elsevier.
Monteiro, S. and Ribeiro, V. (2017) “The balanced scorecard as a tool for environmental management: Approaching the business context to the public sector,” Management of Environmental Quality: An International Journal. Emerald Publishing Limited, 28(3), pp. 332–349.
Naini, S. G. J., Aliahmadi, A. R. and Jafari-Eskandari, M. (2011) “Designing a mixed performance measurement system for environmental supply chain management using evolutionary game theory and balanced scorecard: A case study of an auto industry supply chain,” Resources, conservation and recycling. Elsevier, 55(6), pp. 593–603.
Nash, J. (1951) “19.96. Essays on Game Theory.” Cheltenham, United Kingdom: Edward Elgar.
Neely, A. and Hii, J. (1998) “Innovation and business performance: a literature review,” The Judge Institute of Management Studies, University of Cambridge, pp. 0–65.
Neslin, S. A. and Greenhalgh, L. (1983) “Nash’s theory of cooperative games as a predictor of the outcomes of buyer-seller negotiations: An experiment in media purchasing,” Journal of Marketing Research. SAGE Publications Sage CA: Los Angeles, CA, 20(4), pp. 368–379.
von Neumann, J. and Morgenstern, O. (1944) “Theory of games and economic behavior, Science Editions, 1964.” New York: John Wiley & Sons, Inc.
Othman, R. (2006) “Balanced scorecard and causal model development: preliminary findings,” Management Decision. Emerald Group Publishing Limited, 44(5), pp. 690–702.
Pfeffer, J. and Sutton, R. I. (2000) The knowing-doing gap: How smart companies turn knowledge into action. Harvard business press.
Prasad, S., Shankar, R. and Roy, S. (2019) “Impact of bargaining power on supply chain profit allocation: a game-theoretic study,” Journal of Advances in Management Research. Emerald Publishing Limited.
Quezada, L. E. and López-Ospina, H. A. (2014) “A method for designing a strategy map using AHP and linear programming,” International Journal of Production Economics. Elsevier, 158, pp. 244–255.
Richmond, B. (2001) “A new language for leveraging scorecard-driven learning,” Harvard Business School Publishing. Balanced Scorecard Report.
Rickards, R. C. (2003) “Setting benchmarks and evaluating balanced scorecards with data envelopment analysis,” Benchmarking: An International Journal. MCB UP Ltd.
Safari, G., Hafezalkotob, A. and Khalilzadeh, M. (2018) “A Nash bargaining model for flow shop scheduling problem under uncertainty: a case study from tire manufacturing in Iran,” The International Journal of Advanced Manufacturing Technology. Springer, 96(1–4), pp. 531–546.
Sánchez Torres, J. A., Rivera González, J. A. and Jorba, L. (2018) “What kind of e-mail information is more effective in communicating with the client? Application of game theory,” Harvard Deusto Business Research, 2018, vol. 7, num. 1, p. 2-18. Harvard Deusto Business Review y EAE Business School.
Saraj, M. and Safaei, N. (2012) “Solving bi-level programming problems on using global criterion method with an interval approach,” Applied Mathematical Sciences, 6(23), pp. 1135–1141.
Seyedhosseini, S. M. et al. (2011) “Extracting leanness criteria by employing the concept of Balanced Scorecard,” Expert Systems with Applications. Elsevier, 38(8), pp. 10454–10461.
Shan, H., Yang, K. and Shi, J. (2019) “A Strategic Perspective Analysis for Improving Operational Inefficiency of E-commerce Based on Integrated BSC and Super-SBM Model,” in Proceedings of the 2019 3rd International Conference on Management Engineering, Software Engineering and Service Sciences. ACM, pp. 128–134.
Shafia, M. A. et al. (2018) “A Novel Model for the Analysis of Interactions Between Governments and Agricultures in a Study of Social Beneficial Externalities Based on the Stackelberg Game: A Case Study on Cotton Production,” Journal of Optimization in Industrial Engineering. QIAU, 11(2), pp. 119–127.
Sohn, M. H. et al. (2003) “Corporate strategies, environmental forces, and performance measures: a weighting decision support system using the k-nearest neighbor technique,” Expert Systems with Applications. Elsevier, 25(3), pp. 279–292.
Taylor, M. et al. (2019) “Game theory modelling of retail marketing discount strategies,” Marketing Intelligence & Planning. Emerald Publishing Limited.
Della Vecchia, P. et al. (2019) “Application of Game Theory and Evolutionary Algorithm to the Regional Turboprop Aircraft Wing Optimization,” in Evolutionary and Deterministic Methods for Design Optimization and Control With Applications to Industrial and Societal Problems. Springer, pp. 403–418.
Wang, M. and Li, Y. (2014) “Supplier evaluation based on Nash bargaining game model,” Expert Systems with Applications. Elsevier, 41(9), pp. 4181–4185.
Xiaohui, N. et al. (2014) “Predicting the protein solubility by integrating chaos games representation and entropy in information theory,” Expert Systems with Applications. Elsevier, 41(4), pp. 1672–1679.
Yazdanpanah, A. H., Akbari, A. A. and Mozafari, M. (2019) “A Game Theoretical Approach to Optimize Policies of Government Under the Cartel of Two Green and Non-green Supply Chains,” Journal of Optimization in Industrial Engineering. QIAU, 12(2), pp. 189–197.
Yüksel, İ. and Dağdeviren, M. (2010) “Using the fuzzy analytic network process (ANP) for Balanced Scorecard (BSC): A case study for a manufacturing firm,” Expert Systems with Applications. Elsevier, 37(2), pp. 1270–1278.
Zameer, H. et al. (2018) “A game-theoretic strategic mechanism to control brand counterfeiting,” Marketing Intelligence & Planning. Emerald Publishing Limited, 36(5), pp. 585–600.