Incompetence and impact of training in bimatrix games

Justin Beck, Vladimir Ejov, Jerzy Filar

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    The concept of games with incompetence has been introduced to better represent games where players may not be capable of executing strategies that they select. In particular this paper introduces incompetence into bimatrix games and investigates the properties of such games. The results obtained describe both the general dependence of "extreme Nash equilibrium payoffs" on incompetence and special behaviour arising in particular cases. The dependence of the payoffs can be complex and include non-linearities and transition points. Transition points occur when kernels change and may result in the number of "extreme Nash equilibria" changing. Understanding these changes allows the determination of the benefits of regimes that seek to decrease a player's incompetence. While the games we consider are normally static, in our context there is a hidden dynamics resulting from the fact that players will strive to improve their equilibrium payoffs by changing their incompetence levels. This might require training, in the case of games like tennis, or it might require the purchase of new equipment costing billions of dollars, in the case of military applications.

    Original languageEnglish
    Pages (from-to)2400-2408
    Number of pages9
    JournalAutomatica
    Volume48
    Issue number10
    DOIs
    Publication statusPublished - 2012

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