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Set-weighted games and their application to the cover problem

Author

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  • Vasily V. Gusev

    (National Research University Higher School of Economics)

Abstract

The cover of a transport, social, or communication network is a computationally complex problem. To deal with it, this paper introduces a special class of simple games in which the set of minimal winning coalitions coincides with the set of least covers. A distinctive feature of such a game is that it has a weighted form, in which weights and quota are sets rather than real numbers. This game class is termed set-weighted games. A real-life network has a large number of least covers, therefore this paper develops methods for analyzing set-weighted games in which the weighted form is taken into account. The necessary and sufficient conditions for a simple game to be a set-weighted game were found. The vertex cover game (Gusev, 2020) was shown to belong to the set-weighted game class, and its weighted form was found. The set-weighted game class has proven to be closed under operations of union and intersection, which is not the case for weighted games. The sample object is the transport network of a district in Petrozavodsk, Russia. A method is suggested for efficiently deploying surveillance cameras at crossroads so that all transport network covers are taken into account.

Suggested Citation

  • Vasily V. Gusev, 2021. "Set-weighted games and their application to the cover problem," HSE Working papers WP BRP 247/EC/2021, National Research University Higher School of Economics.
    • Handle: RePEc:hig:wpaper:247/ec/2021
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    References listed on IDEAS

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    More about this item

    Keywords

    simple games; set-weighted games; vertex covergame; cover problem; cooperative generating functions; power indexes;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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