Geodesic
The ''attack-defense'' model on networks with the initial residuals of the parties
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2021), pp. 68-81

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The article generalizes the "attack-defense" game with the network structure, in terms of accounting for the initial residuals of the parties' resources and is based on the work by Hohzaki and Tanaka. In contrast to the latter, the defense on each of the possible movement directions between the network’s vertices, given by the oriented edges, can have nonzero initial residuals of the parties' resources, which generally leads to convex minimax problems that can be solved by the subgradient descent method. In particular, the model under study generalizes the "attack-defense" game with initial residuals, proposed by Ogaryshev, to the network case.
Keywords: Germeier’s classic "attack-defense" game, Ogaryshev’s generalization, network generalization by Hohzaki and Tanaka, best guaranteed defense result, minimax defense strategy, mixed attack strategy. 
@article{VTPMK_2021_2_a5,
     author = {A. G. Perevozchikov and V. Yu. Reshetov and A. I. Lesik},
     title = {The ''attack-defense'' model on networks with the initial residuals of the parties},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {68--81},
     publisher = {mathdoc},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2021_2_a5/}
}
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A. G. Perevozchikov; V. Yu. Reshetov; A. I. Lesik. The ''attack-defense'' model on networks with the initial residuals of the parties. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2021), pp. 68-81. http://geodesic.mathdoc.fr/item/VTPMK_2021_2_a5/