Advertisement

Intelligent Interaction Modelling: Game Theory

  • Laobing Zhang
  • Genserik Reniers
Chapter
Part of the Advanced Sciences and Technologies for Security Applications book series (ASTSA)

Abstract

Game theory is a mathematical tool for supporting decision making in a multiple players situation where one player’s utility will be determined not only by his own decision, but also by other players’ decisions. An illustrative example of this situation is the Rock/Scissors/Paper game (“RSP” game). In an RSP game, whether a player wins or loses depends on both what he plays and what his opponent plays. This is a well-known game between mostly children with very simple rules. Two ‘players’ hold their right hands out simultaneously at an agree signal to represent a rock (closed fist), a piece of paper (open palm), or a pair of scissors (first and second fingers held apart). If the two symbols are the same, it’s a draw. Otherwise rock blunts scissors, paper wraps rock, and scissors cut paper, so the respective winners for these three outcomes are rock, paper and scissors. The RSP game is what is called a ‘two-player zero-sum non-cooperative’ game. There are obviously many other types of game and the field of game theory is very powerful to provide (mathematical) insights into strategic decision-making.

References

  1. 1.
    Von Neumann J, Morgenstern O. Theory of games and economic behavior. Princeton: Princeton University Press; 2007.Google Scholar
  2. 2.
    Nash JF. Equilibrium points in n-person games. Proc Nat Acad Sci USA. 1950;36(1):48–9.CrossRefGoogle Scholar
  3. 3.
    Harsanyi JC. Games with incomplete information played by “Bayesian” players, i–iii: part i. the basic model. Manag Sci. 2004;50((12_suppl)):1804–17.CrossRefGoogle Scholar
  4. 4.
    Lemke CE, Howson J, Joseph T. Equilibrium points of bimatrix games. J Soc Ind Appl Math. 1964;12(2):413–23.CrossRefGoogle Scholar
  5. 5.
    Chen X, Deng X, editors. Settling the complexity of two-player Nash equilibrium. Foundations of Computer Science, 2006 FOCS’06 47th Annual IEEE Symposium on; 2006: IEEE.Google Scholar
  6. 6.
    Nisan N, Roughgarden T, Tardos E, Vazirani VV. Algorithmic game theory. Cambridge: Cambridge University Press; 2007.CrossRefGoogle Scholar
  7. 7.
    101 GT. The support of mixed strategies. Available from: http://gametheory101.com/courses/game-theory-101/support-of-mixed-strategies/
  8. 8.
    Rios J, Insua DR. Adversarial risk analysis for counterterrorism modeling. Risk Anal. 2012;32(5):894–915.CrossRefGoogle Scholar
  9. 9.
    Kelly A. Decision making using game theory: an introduction for managers. Cambridge: Cambridge University Press; 2003.CrossRefGoogle Scholar
  10. 10.
    Friedman M. Essays in positive economics. Chicago: University of Chicago Press; 1953.Google Scholar
  11. 11.
    Osborne MJ. An introduction to game theory. New York: Oxford University Press; 2004.Google Scholar
  12. 12.
    Pita J, Jain M, Tambe M, Ordóñez F, Kraus S. Robust solutions to Stackelberg games: addressing bounded rationality and limited observations in human cognition. Artif Intell. 2010;174(15):1142–71.CrossRefGoogle Scholar
  13. 13.
    Skaperdas S. Contest success functions. Econ Theory. 1996;7(2):283–90.CrossRefGoogle Scholar
  14. 14.
    Tambe M. Security and game theory: algorithms, deployed systems, lessons learned. New York: Cambridge University Press; 2011.CrossRefGoogle Scholar
  15. 15.
    Nikoofal ME, Zhuang J. Robust allocation of a defensive budget considering an attacker’s private information. Risk Anal. 2012;32(5):930–43.CrossRefGoogle Scholar
  16. 16.
    Von Stengel B, Zamir S. Leadership with commitment to mixed strategies. In: CDAM Research Report LSECDAM-2004-01. London School of Economics; 2004.Google Scholar
  17. 17.
    Guikema SD. Game theory models of intelligent actors in reliability analysis: an overview of the state of the art. Game theoretic risk analysis of security threats. New York: Springer; 2009. p. 13–31.Google Scholar
  18. 18.
    Zhang R. A game-theoretical model to improve process plant protection from terrorist attacks. Risk Anal. 2016;36(12):2285–97.CrossRefGoogle Scholar
  19. 19.
    Feng Q, Cai H, Chen Z, Zhao X, Chen Y. Using game theory to optimize allocation of defensive resources to protect multiple chemical facilities in a city against terrorist attacks. J Loss Prev Process Ind. 2016;43:614–28.CrossRefGoogle Scholar
  20. 20.
    Zhang L, Reniers G, Chen B, Qiu X. Integrating the API SRA methodology and game theory for improving chemical plant protection. J Loss Prev Process Ind. 2018;51(Suppl C):8–16.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Laobing Zhang
    • 1
  • Genserik Reniers
    • 1
  1. 1.Safety and Security Science GroupDelft University of TechnologyDelftThe Netherlands

Personalised recommendations