Skip to main content

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 283))

Abstract

According to Wasburn and Kress (2009), “military operations are conducted in the presence of uncertainty, much of which is due to the unpredictability of the enemy.” Further they state that there are two fundamental directions to go: game theory or wargaming. We discuss only game theory here in this report. According to Wasburn et al. (2009) in their discussions, they limit analysis to the two-person zero-sum games for two reasons: (1) combat usually involves two opposing sides and (2) the two-person zero-sum solutions methods are more easily generalizable than the partial conflict (nonzero-sum) games.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Barron, E. D. (2013). Game theory an introduction (pp. 156–158). Hoboken, NJ: Wiley.

    Google Scholar 

  • Cantwell, G. (2003). Can two person zero sum game theory improve military decision-making course of action selection? Fort Leavenworth, KS: School of Advanced Military Studies.

    Book  Google Scholar 

  • Feix, M. (2007). Game theory: Toolkit and workbook for defense analysis students. MS Thesis, Naval Postgraduate School.

    Google Scholar 

  • Fox, W. (2016). Applied game theory to improve strategic and tactical military decision theory. J Def Manag, 6, 2. https://doi.org/10.4172/2167-0374.1000147.

  • Fox, W. P. (2010). Teaching the applications of optimization in game theory’s zero-sum and non-zero sum games. International Journal of Data Analysis Techniques and Strategies, 2(3), 258–284.

    Article  Google Scholar 

  • Fox, W. P. (2012a). Mathematical modeling of the analytical hierarchy process using discrete dynamical systems in decision analysis. Computers in Education Journal, 3(3), 27–34.

    Google Scholar 

  • Fox, W. P. (2012b). Mathematical modeling with Maple. Boston, MA: Cengage.

    Google Scholar 

  • Fox, W. P. (2014). Chapter 221, TOPSIS in business analytics. In Encyclopedia of business analytics and optimization (Vol. V(5), pp. 281–291). Hershey, PA: IGI Global and Sage.

    Google Scholar 

  • Fox, W. P. (2015). Two person zero-sum games as an application of linear programming using the excel solver. Computers in Education Journal, 6(3), 37–49.

    Google Scholar 

  • Fox, W., & Thompson, M. N. (2014). Phase targeting of terrorist attacks: simplifying complexity with analytical hierarchy process. International Journal of Decision Sciences, 5(1), 57–64.

    Google Scholar 

  • Gant, J. (2009). A strategy for success in Afghanistan: one tribe at a time. Los Angeles, CA: Nine Sisters Imports.

    Google Scholar 

  • Gillman, R., & Housman, D. (2009). Models of conflict and cooperation. Providence, RI: American Mathematical Society.

    Book  Google Scholar 

  • Giordano, F., Fox, W., & Horton, S. (2014). A first course in mathematical modeling (5th ed.). Boston, MA: Cengage Publishing.

    Google Scholar 

  • Global Data Ltd. (2012, October). Afghanistan’s mining industry on the path of development. London, UK. Retrieved from http://search.proquest.com/

  • Haywood, O. (1954). Military decision and game theory. Journal of the Operations Research Society, 2(4), 365–385.

    Google Scholar 

  • Jensen, N., & Johnston, N. (2011). Political risk, reputation, and the resource curse. Comparative Political Studies, 44, 662–688. https://doi.org/10.1177/0010414011401208.

    Article  Google Scholar 

  • Khatwani, G., & Kar, A. K. (2016). Improving the Cosine Consistency Index for the analytic hierarchy process for solving multi-criteria decision making problems. Applied Computing and Informatics, 13(2), 118–129.

    Article  Google Scholar 

  • Kral, S. (2011, April). Minerals key to Afghanistan. Mining Engineering, 63(4), 136.

    Google Scholar 

  • Lipow, J., & Melese, F. (2011, September). Economic and security implications of Afghanistan’s newly discovered mineral wealth. Defense & Security Analysis, 27(3), 277. Retrieved from http://search.proquest.com/

  • Nash, J. (1950). The bargaining problem. Econometrica, 18, 155–162.

    Article  Google Scholar 

  • Peters, S., Kalaly, S., Chirico, P., & Hubbard, B. (2012). Summaries of the important areas formineral investment and production opportunities of nonfuel minerals in Afghanistan: U.S. Geological Survey Open-File Report 2011-1204. Retrieved from http://pubs.usgs.gov/of/2011/1204/.

  • Saaty, T. (1980). The analytic hierarchy process. New York: McGraw-Hill Book.

    Google Scholar 

  • Schmitt, J. (1994). Mastering tactics: A decision game workbook. Quantico, VA: Marine Corps Gazette.

    Google Scholar 

  • Straffin, P. D. (2004). Game theory and strategy. Washington, DC: Mathematical Association of America.

    Google Scholar 

  • Von Neumann, J., & Morgenstern, O. (2004). Theory of games and economic behavior (60th anniversary ed.). Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Wasburn, A., & Kress, M. (2009). Combat modeling. (International Series in Operations Research & Management Science) 2009th Edition. New York: Springer.

    Google Scholar 

  • Winston, W. (1995). Introduction to mathematical programming; Applications and algorithms. Belmont, CA: Thomson.

    Google Scholar 

  • Winston, W. L. (2003). Introduction to mathematical programming (4th ed.). Belmont, CA, Duxbury Press.

    Google Scholar 

Suggested Reading

  • Aumann, R. J. (1987). Game theory. In The New Palgrave: A dictionary of economics. London: Palgrave Macmillan.

    Google Scholar 

  • Bazarra, M. S., Sherali, H. D., & Shetty, C. M. (2006). Nonlinear programming (3rd ed.). New York: Wiley.

    Book  Google Scholar 

  • Braun, S. J. (1994). Theory of moves. American Scientist, 81, 562–570.

    Google Scholar 

  • Camerer, C. (2003). Behavioral game theory: experiments in strategic interaction, Russell Sage Foundation, description and introduction (pp. 1–25).

    Google Scholar 

  • Chiappori, A., Levitt, S., & Groseclose, P. (2002). Testing mixed-strategy equilibria when players are heterogeneous: The case of penalty kicks in soccer. American Economic Review, 92(4), 1138–1151.

    Article  Google Scholar 

  • Crawford, V. (1974). Learning the optimal strategy in a zero-sum game. Econometrica, 42(5), 885–891.

    Article  Google Scholar 

  • Danzig, G. (1951). Maximization of a linear unction of variables subject to linear inequalities. In T. Koopman (Ed.), Activity analysis of production and allocation conference proceeding (pp. 339–347). New York: Wiley.

    Google Scholar 

  • Danzig, G. (2002). Linear programming. Operations Research, 50(1), 42–47.

    Article  Google Scholar 

  • Dixit, A., & Nalebuff, B. (1991). Thinking strategically: The competitive edge in business, politics, and everyday life. New York: W.W. Norton.

    Google Scholar 

  • Dorfman, R. (1951). Application of the simplex method to a game theory problem. In T. Koopman (Ed.), Activity analysis of production and allocation conference proceeding (pp. 348–358). New York: Wiley.

    Google Scholar 

  • Dutta, P. (1999). Strategies and games: theory and practice. Cambridge, MA: MIT Press.

    Google Scholar 

  • Fox, W. P. (2008). Mathematical modeling of conflict and decision making: The writer’s guild strike 2007–2008. Computers in Education Journal, 18(3), 2–11.

    Google Scholar 

  • Fox, W. P., & Everton, S. (2013). Mathematical modeling in social network analysis: Using TOPSIS to find node influences in a social network. Journal of Mathematics and Systems Science, 3(2013), 531–541.

    Google Scholar 

  • Fox, W. P., & Everton, S. (2014a). Mathematical modeling in social network analysis: using data envelopment analysis and analytical hierarchy process to find node influences in a social network. Journal of Defense Modeling and Simulation, 2014, 1–9.

    Google Scholar 

  • Fox, W., & Everton, S. (2014b). Using mathematical models in decision making methodologies to find key nodes in the noordin dark network. American Journal of Operations Research, 2014, 1–13.

    Google Scholar 

  • Gale, D., Kuhn, H., & Tucker, A. (1951). Linear programming and the theory of games). In T. Koopman (Ed.), Activity analysis of production and allocation conference proceeding (pp. 317–329). New York: Wiley.

    Google Scholar 

  • Gintis, H. (2000). Game theory evolving: a problem-centered introduction to modeling strategic behavior. Princeton, NJ: University Press.

    Google Scholar 

  • Harrington, J. (2008). Games, strategies, and decision making. New York: Worth.

    Google Scholar 

  • Isaacs, R. (1999). Differential games: A mathematical theory with applications to warfare and pursuit, control and optimization. New York: Dover.

    Google Scholar 

  • Kilcullen, D. (2009, March 13). The accidental guerilla: fighting small wars in the midst of a big one. Oxford: Oxford University Press.

    Google Scholar 

  • Kim, H. (2014). China’s position on Korean unification and ROK-PRC relations. 전략연구 (Feb, 2014). pp 235–257. Retrieved from http://www.dbpia.co.kr/view/ar_view.asp?arid=2501730

  • Kim, S. (2015). The day after: ROK-U.S. cooperation for Korean unification. The Washington Quarterly, 38(3), 37–58. https://doi.org/10.1080/0163660X.2015.1099024.

    Article  Google Scholar 

  • Khatwani, G., Singh, S. P., Trivedi, A., & Chauhan, A. (2015). Fuzzy-TISM: A fuzzy extension of TISM for group decision making. Global Journal of Flexible Systems Management, 16(1), 97–112.

    Article  Google Scholar 

  • Klarrich, E. (2009). The mathematics of strategy. Classics of the Scientific Literature. Retrieved October, 2009 from www.pnas.org/site/misc/classics5.shtml.

  • Kuhn, H. W., & Tucker, A. W. (1951). Nonlinear programming. In J. Newman (Ed.), Proceedings of the second Berkley symposium on mathematical statistics and probability. Berkeley, CA: University of California Press.

    Google Scholar 

  • Leyton-Brown, K., & Shoham, Y. (2008). Essentials of game theory: A concise, multidisciplinary introduction. San Rafael, CA: Morgan & Claypool.

    Book  Google Scholar 

  • Miller, J. (2003). Game theory at work: how to use game theory to outthink and outmaneuver your competition. New York: McGraw-Hill.

    Google Scholar 

  • Myerson, R. B. (1991). Game theory: Analysis of conflict. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Nash, J. (1951). Non-cooperative games. Annals of Mathematics, 54, 289–295.

    Article  Google Scholar 

  • Nash, J. (2009). Lecture at NPS. Feb 19, 2009.

    Google Scholar 

  • Nash, J. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America, 36(1), 48–49.

    Article  Google Scholar 

  • North Korea Declares 1953 Armistice Invalid. (2013). CNN Wire, Mar 11, 2013.

    Google Scholar 

  • Osborne, M. (2004). An introduction to game theory. Oxford: Oxford University Press.

    Google Scholar 

  • Papayoanou, P. (2010). Game theory for business, e-book. Gainesville, FL: Probabilistic Publishing Retrieved from http://www.decisions-books.com/Links.html.

    Google Scholar 

  • Rasmusen, E. (2006). Games and information: An introduction to game theory (4th ed.). New York: Wiley-Blackwell.

    Google Scholar 

  • Shoham, Y., & Leyton-Brown, K. (2009). Multiagent systems: Algorithmic, game- theoretic and logical foundations. New York: Cambridge University Press.

    Google Scholar 

  • Smith, M. (1982). Evolution and the theory of games. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Smith, J. M., & Price, G. (1973). The logic of animal conflict. Nature, 246(5427), 15–18.

    Article  Google Scholar 

  • Straffin, P. (1980). The prisoner’s dilemma. UMAP Journal, 1, 101–113.

    Google Scholar 

  • Straffin, P. (1989). Game theory and nuclear deterrence. UMAP Journal, 10, 87–92.

    Google Scholar 

  • Straffin, P. (2003). Game theory and strategy. Washington, DC: The Mathematical Association of America. Chapter 19.

    Google Scholar 

  • Williams, J. D. (1986). The compleat strategyst. New York: Dover.

    Google Scholar 

  • Webb, J. N. (2007). Game theory: decisions, interaction and evolution. London: Springer.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Fox, W.P., Burks, R. (2019). Game Theory. In: Applications of Operations Research and Management Science for Military Decision Making. International Series in Operations Research & Management Science, vol 283. Springer, Cham. https://doi.org/10.1007/978-3-030-20569-0_6

Download citation

Publish with us

Policies and ethics