Set-weighted games and their application to the cover problem

Vasily V. Gusev

European Journal of Operational Research, 2023, vol. 305, issue 1, 438-450

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.

Keywords: Game theory; Simple games; Set-weighted games; Cover problem; Cooperative generating functions (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:305:y:2023:i:1:p:438-450

DOI: 10.1016/j.ejor.2022.05.026

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