Games, Incompetence, and Training

  • Justin Beck
  • Jerzy A. Filar
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 9)


In classical noncooperative matrix games the payoffs are determined directly by the players’ choice of strategies. In reality, however, a player may not be capable of executing his or her chosen strategy due to a lack of skill that we shall refer to as incompetence. A method for analysing incompetence in matrix games is introduced, examined and demonstrated. Along with the derivation of general characteristics, a number of interesting special behaviours are identified. These special behaviours are shown to be the result of particular forms of the game and/or of the incompetence matrices. The development of this simple model was motivated by applications where a decision to increase competence is to be evaluated. Investments that decrease incompetence (such as training) need to be related to the change in the value of the game. A game theory approach is used since possible changes in strategies used by other players must be considered. An analogy with the game of tennis is discussed, as is an analogy with capability investment decisions in the military.


Payoff Matrix Tennis Player Matrix Game Single Player Extensive Form Game 
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  1. [1]
    D. Billings, N. Burch, A. Davidson, R. Holte, J. Schaeffer, T. Schauenberu and D. Szafron. Approximating game-theoretic optimal strategies for fullscale poker. In Proceedings of the 18th International Conference on Artificial Intelligence, 2003.Google Scholar
  2. [2]
    M. Walker and J. Wooders. Minimax play at Wimbledon. The American Econmic Review 9151521–1538 2001Google Scholar
  3. [3]
    O. G. Haywood Jr. Military decision and game theory. Operations Research, 2(4):365–385, 1954.Google Scholar
  4. [4]
    D. R. Fulkerson and S. M. Johnson. Atactical air game. Operations Research, 5(5):704–712, Oct 1957.MathSciNetCrossRefGoogle Scholar
  5. [5]
    R. Selten. Reexamination of the perfectness concept for equilibrium points in extensive games. Intl Journal of Game Theory 4125–55 1975Google Scholar
  6. [6]
    C. Stothard and R. Nicholson. Skill acquisition and retention in training. Technical Report DSTO-CR-0218, Defence Science and Technology Organisation, Edinburgh, South Australia, December 2001.Google Scholar
  7. [7]
    G. Owen. Game Theory. W. B. Saunders Company, Philadelphia, PA, 1968.MATHGoogle Scholar
  8. [8]
    J. A. Filar and K. Vrieze. Competitive Markov Decision Processes. Springer-Verlag, New York, 1996.Google Scholar
  9. [9]
    L. S. Shapley and R. N. Sw. Basic solutions of discrete games. Annals of Mathematics Study 12427–35 1950Google Scholar
  10. [10]
    J. A. Filar. Semi-antagonistic equilibrium points and action costs. Cahiers du C.E.R.O. 253-4227–239 1984Google Scholar

Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • Justin Beck
    • 1
  • Jerzy A. Filar
    • 2
  1. 1.Defence Systems Analysis DivisionDefence Science and Technology OrganisationEdinburghAustralia
  2. 2.Centre for Industrial and Applied MathematicsUniversity of South AustraliaAdelaideAustralia

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