A Game Theory Approach for Deploying Medical Resources in Emergency Department

  • Cheng-Kuang Wu
  • Yi-Ming Chen
  • Dachrahn Wu
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 758)


Emergency department need a decision support tool to advise the critical medical resources (such as doctors, nurses, or beds) to urgent patients in the different service time requirements. This study proposes a framework for emergency response service that incorporates two game theory models designed to deploy response medical resources when raising three threat advisory levels. First, the interactions between a group of weekly patients and a response agent of emergency department are modeled as a non-cooperative game, after which a threat, vulnerability, and consequence value (i.e., TVC) of each type of patients for emergency event is derived from Nash equilibrium of game. Second, four TVC values of emergency events are utilized for computation of the Shapely value for each type of patient. The deployment of emergency medical resources is carried out based on their expected marginal contribution. Then, the model scheduled daily physicians, nurses, and beds in emergency department. The experimental results show that proposal model is feasible as a method to improve efficiency in emergency department.


Emergency response Nash equilibrium Shapley value Medical resources scheduling 


  1. 1.
    Cox Jr., L.A.: Game theory and risk analysis. Risk Anal. 29(8), 1062–1068 (2009)CrossRefGoogle Scholar
  2. 2.
    Dixit, A., Skeath, S.: Games of Strategy, p. 574. W.W. Norton & Company, New York (2007)Google Scholar
  3. 3.
    Ghanes, K., Wargon, M., Jouini, O., Jemai, Z., Diakogiannis, A., Hellmann, R., et al.: Simulation-based optimization of staffing levels in an emergency department. Simul. Trans. Soc. Model. Simul. Int. 91(10), 942–953 (2015)Google Scholar
  4. 4.
    Gorelick, M.H., Yen, K., Yun, H.J.: The effect of in-room registration on emergency department length of stay. Ann. Emerg. Med. 45(2), 128–133 (2005)CrossRefGoogle Scholar
  5. 5.
    Hansen, T.: On the approximation of Nash equilibrium points in an n-person non-cooperative game. SIAM J. Appl. Math. 26(3), 622–637 (1974)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Hoot, N.R., Zhou, C., Jones, I., Aronsky, D.: Measuring and forecasting emergency department crowding in real time. Ann. Emerg. Med. 49(6), 747–755 (2007)CrossRefGoogle Scholar
  7. 7.
    Jacobson, E.U., Argon, N.T., Ziya, S.: Priority assignment in emergency response. Oper. Res. 60(60), 813–832 (2012)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Kuo, Y.H., Leung, J.M.Y., Graham, C.A.: Simulation with data scarcity: developing a simulation model of a hospital emergency department. In: Proceedings of the Winter Simulation Conference (WSC), pp. 1–12 (2012)Google Scholar
  9. 9.
    Larkin, G.L., Weber, J.E., Moskop, J.C.: Resource utilization in the emergency department: the duty of stewardship. J. Emerg. Med. 16(3), 499–503 (1998)CrossRefGoogle Scholar
  10. 10.
    Lemke, C.E., Howson, J.T.: Equilibrium points of bimatrix games. SIAM J. Appl. Math. 12, 413–423 (1964)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Lewis, H.W.: Why Flip a Coin? The Art and Science of Good Decisions. Wiley, New York (1997)Google Scholar
  12. 12.
    Luscombe, R., Kozan, E.: Dynamic resource allocation to improve emergency department efficiency in real time. Eur. J. Oper. Res. 255(2), 593–603 (2016)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Mishra, D., Rangarajan, B.: Cost sharing in a job scheduling problem using the shapley value. In: Proceedings of the 6th ACM Conference on Electronic Commerce, pp. 232–239 (2005)Google Scholar
  14. 14.
    Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, London (1994)MATHGoogle Scholar
  15. 15.
    Owen, G.: Game Theory, 3rd edn, p. 265. Academic Press, New York (2001)Google Scholar
  16. 16.
    Parsons, S., Wooldridge, M.: Game theory and decision theory in multi-agent systems. Autonom. Agents Multi Agent Syst. 5, 243–254 (2002)CrossRefMATHGoogle Scholar
  17. 17.
    Ranganathan, N., Gupta, U., Shetty, R., Murugavel, A.: An automated decision support system based on game theoretic optimization for emergency management in urban environments. J. Homel. Secur. Emerg. Manag. 4(2), Article 1 (2007).
  18. 18.
    Ruger, J.P., Lewis, L.M., Richter, C.J.: Patterns and factors associated with intensive use of ED services: implications for allocating resources. Am. J. Emerg. Med. 30(9), 1884–1894 (2012)Google Scholar
  19. 19.
    Shin, S.Y., Balasubramanian, H., Brun, Y., Henneman, P.L., Osterweil, L.J.: Resource scheduling through resource-aware simulation of emergency departments. In: International Workshop on Software Engineering in Health Care, vol. 7789, pp. 64–70 (2013)Google Scholar
  20. 20.
    Xiao, J., Osterweil, L.J., Wang, Q.: Dynamic scheduling of emergency department resources. In: ACM International Health Informatics Symposium, pp. 590–599 (2010)Google Scholar
  21. 21.
    Zolezzi, J.M., Rudnick, H.: Transmission cost allocation by cooperative games and coalition formation. IEEE Power Eng. Rev. 17(4), 1008–1015 (2002)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Zhejiang Industry & Trade Vocational CollegeWenzhouChina
  2. 2.Department of Information ManagementNational Central UniversityTaoyuanTaiwan
  3. 3.Department of EconomicsNational Central UniversityTaoyuanTaiwan

Personalised recommendations