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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">vmait</journal-id><journal-title-group><journal-title xml:lang="ru">Computational Mathematics and Information Technologies</journal-title><trans-title-group xml:lang="en"><trans-title>Computational Mathematics and Information Technologies</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">2587-8999</issn><publisher><publisher-name>Донской государственный технический университет</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.23947/2587-8999-2022-1-3-104-120</article-id><article-id custom-type="elpub" pub-id-type="custom">vmait-13</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>ИГРА БЛОТТО В ПРОПАГАНДИСТСКОЙ БИТВЕ</article-title><trans-title-group xml:lang="en"><trans-title>BLOTTO GAME IN A PROPAGANDA BATTLE</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Подлипская</surname><given-names>О. Г</given-names></name><name name-style="western" xml:lang="en"><surname>Podlipskaia</surname><given-names>O. G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ольга Геннадьевна Подлипская, Кафедра высшей математики, доцент</p><p>141701, Московская облаcть, г. Долгопрудный, Институтский пер., 9</p></bio><bio xml:lang="en"><p>Olga Podlipskaia, Department of Higher Mathematics, Associate Professor</p><p>9 Institutskiy per., Dolgoprudny, Moscow Region, 141701, Russian Federation</p></bio><email xlink:type="simple">podlipskaya.og@phystech.edu</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Московский физико-технический институт (национальный исследовательский университет)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Moscow Institute of Physics and Technology</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>20</day><month>02</month><year>2023</year></pub-date><volume>6</volume><issue>3</issue><fpage>114</fpage><lpage>112</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Подлипская О.Г., 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder xml:lang="ru">Подлипская О.Г.</copyright-holder><copyright-holder xml:lang="en">Podlipskaia O.G.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.cmit-journal.ru/jour/article/view/13">https://www.cmit-journal.ru/jour/article/view/13</self-uri><abstract><p>В работе рассматривается следующий процесс. Две партии, вовлечены в информационную войну по двум темам, которые понимаются как поля сражений. Каждая сторона имеет ограниченный ресурс вещания для пропаганды, и распределяет свой ресурс между этими двумя темами. Каждый индивид поддерживает одну из сторон по каждой теме. Если индивид поддерживает разные партии по разным темам, то он считается сторонником партии, которую он поддерживает по более значимой теме. Сторонники партии участвуют в партиципаторной пропаганде, проводя кампанию по одной или обеим темам, по которым они поддерживают свою партию. Значимость темы зависит от объема вещания СМИ по ней. Число сторонников партии меняется с течением времени под влиянием средств массовой информации и партийной пропаганды. Задача заключается в том, чтобы определить наилучшие стратегии сторон.</p><p>Каждая сторона распределяет свой вещательный ресурс между двумя темами, тем самым выбирая свою стратегию. Таким образом, появляется игра Блотто, т.е. игра двух игроков с нулевой суммой, в которой игроки распределяют ограниченные ресурсы по нескольким полям сражений. В этой матричной игре выигрыш партий – это количество их сторонников в конце пропагандистской битвы. Были проведены численные эксперименты, в ходе которых эти выигрыши были численно рассчитаны.</p><p>Как правило, наилучшими стратегиями являются те, в которых ресурсы распределяются между темами неравномерно. Более того, часто лучшая стратегия – потратить все ресурсы на одну тему.</p></abstract><trans-abstract xml:lang="en"><p>The model describes the following process. Two parties, called Left and Right, are involved in information warfare on two topics that play the role of battlefields. Each party has limited broadcasting resources for propaganda, which each allocates between these two topics. Each member of the population backs one of the parties for each topic. A situation is possible in which an individual backs different parties on different topics. In this case, the individual is considered a supporter of the party supported on a more salient topic. Party supporters participate in participatory propaganda, campaigning on the topic or two topics they support for their party. The saliency of a topic depends on the amount of media broadcasting and communication on it. The number of party supporters’ changes over time under the influence of media and party propaganda. The problem is to determine the parties' best strategies.</p><p>Each party apportion its broadcasting resource between two topics, thereby choosing its strategy. Therefore, a Blotto game appears. The Blotto game is a two-player zero-sum game in which the players distribute limited resources over several battlefields. In this matrix game, payoffs of the parties are the numbers of their supporters at the end of the propaganda battle. Numerical experiments were conducted in which these payoffs were calculated numerically and the obtained game was solved.</p><p>Typically, the best strategies are those where the resource is allocated between the topics very unevenly. Moreover, often the best strategy is spending all the resource on one topic.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>игра Блотто</kwd><kwd>пропагандистская битва</kwd><kwd>математическая модель</kwd><kwd>оптимальная стратегия</kwd><kwd>численный эксперимент</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Blotto game</kwd><kwd>propaganda battle</kwd><kwd>mathematical model</kwd><kwd>optimal strategy</kwd><kwd>numerical experiment</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено при финансовой поддержке РФФИ в рамках научного проекта № 20-01-00229.</funding-statement><funding-statement xml:lang="en">The research was supported by Russian Foundation for Basic Research (project 20-01-00229).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">McCombs, M., Stroud, N.J.: Psychology of agenda-setting effects: Mapping the paths of information processing. Review of Communication Research, 2(1), 2014, pp. 68-93.</mixed-citation><mixed-citation xml:lang="en">McCombs, M., Stroud, N.J.: Psychology of agenda-setting effects: Mapping the paths of information processing. Review of Communication Research, 2(1), 2014, pp. 68-93.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Alkhodair, S. A., Ding, S. H., Fung, B. C., &amp; Liu, J. Detecting breaking news rumors of emerging topics in social media. Information Processing &amp; Management, 57(2), 2020, pp. 102018.</mixed-citation><mixed-citation xml:lang="en">Alkhodair, S. A., Ding, S. H., Fung, B. C., &amp; Liu, J. Detecting breaking news rumors of emerging topics in social media. Information Processing &amp; Management, 57(2), 2020, pp. 102018.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Wang, Z., Liang, J., Nie, H., Zhao, H. A 3SI3R model for the propagation of two rumors with mutual promotion. Advances in Difference Equations, 2020, 1, pp. 1-19.</mixed-citation><mixed-citation xml:lang="en">Wang, Z., Liang, J., Nie, H., Zhao, H. A 3SI3R model for the propagation of two rumors with mutual promotion. Advances in Difference Equations, 2020, 1, pp. 1-19.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Xiao, Y., Yang, Q., Sang, C., Liu, Y. Rumor diffusion model based on representation learning and anti-rumor. IEEE Transactions on Network and Service Management, 2020, 17(3), pp. 1910-1923.</mixed-citation><mixed-citation xml:lang="en">Xiao, Y., Yang, Q., Sang, C., Liu, Y. Rumor diffusion model based on representation learning and anti-rumor. IEEE Transactions on Network and Service Management, 2020, 17(3), pp. 1910-1923.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">A.P. Mikhailov, G.B. Pronchev, O.G. Proncheva. Mathematical Modeling of Information Warfare in Techno-Social Environments // Techno-Social Systems for Modern Economical and Governmental Infrastructures. IGI Global, 2019. pp. 174-210. DOI: 10.4018/978-1-5225-5586-5.ch008.</mixed-citation><mixed-citation xml:lang="en">A.P. Mikhailov, G.B. Pronchev, O.G. Proncheva. Mathematical Modeling of Information Warfare in Techno-Social Environments // Techno-Social Systems for Modern Economical and Governmental Infrastructures. IGI Global, 2019. pp. 174-210. DOI: 10.4018/978-1-5225-5586-5.ch008.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Chkhartishvili, A.G., Gubanov, D.A. and Novikov, D.A. Social Networks: Models of Information Influence, Control and Confrontation, Springer, 2018, Vol. 189.</mixed-citation><mixed-citation xml:lang="en">Chkhartishvili, A.G., Gubanov, D.A. and Novikov, D.A. Social Networks: Models of Information Influence, Control and Confrontation, Springer, 2018, Vol. 189.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">.V. Kozitsin, A general framework to link theory and empirics in opinion formation models, Scientific reports, 2022, Vol. 12, p. 5543.</mixed-citation><mixed-citation xml:lang="en">.V. Kozitsin, A general framework to link theory and empirics in opinion formation models, Scientific reports, 2022, Vol. 12, p. 5543.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">I.V. Kozitsin, Formal models of opinion formation and their application to real data: evidence from online social networks, The Journal of Mathematical Sociology, 2022, 46(2), pp. 120-47.</mixed-citation><mixed-citation xml:lang="en">I.V. Kozitsin, Formal models of opinion formation and their application to real data: evidence from online social networks, The Journal of Mathematical Sociology, 2022, 46(2), pp. 120-47.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">A.G. Chkhartishvili, D.A. Gubanov, On the Concept of an Informational Community in a Social Network, Journal of Physics: Conference Series, 2021, Vol. 1864, No. 1, pp. 012052.</mixed-citation><mixed-citation xml:lang="en">A.G. Chkhartishvili, D.A. Gubanov, On the Concept of an Informational Community in a Social Network, Journal of Physics: Conference Series, 2021, Vol. 1864, No. 1, pp. 012052.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Boldyreva, A., Sobolevskiy, O., Alexandrov, M., Danilova,V. Creating collections of descriptors of events and processes based on Internet queries, In: Proc. of 14-th Mexican Intern. Conf. on Artif. Intell. (MICAI-2016), Springer Cham, LNAI, Vol. 10061, (chapter 26), 2016, pp. 303-314.</mixed-citation><mixed-citation xml:lang="en">Boldyreva, A., Sobolevskiy, O., Alexandrov, M., Danilova,V. Creating collections of descriptors of events and processes based on Internet queries, In: Proc. of 14-th Mexican Intern. Conf. on Artif. Intell. (MICAI-2016), Springer Cham, LNAI, Vol. 10061, (chapter 26), 2016, pp. 303-314.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">V. Danilova, S. Popova, M. Alexandrov, “Multilingual Protest Event Data Collection with GATE,” Proc. of 21-th Intern. Conf. on Natural Languages and Data Base (NLDB-2016), Springer, Vol. 9612, 2016, pp. 115-126.</mixed-citation><mixed-citation xml:lang="en">V. Danilova, S. Popova, M. Alexandrov, “Multilingual Protest Event Data Collection with GATE,” Proc. of 21-th Intern. Conf. on Natural Languages and Data Base (NLDB-2016), Springer, Vol. 9612, 2016, pp. 115-126.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">A.P. Petrov, S.A. Lebedev. Online Political Flashmob: the Case of 632305222316434 // Computational mathematics and information technologies, 2019, No 1, pp. 17–28. DOI: 10.23947/2587-8999-2019-1-1-17-28.</mixed-citation><mixed-citation xml:lang="en">A.P. Petrov, S.A. Lebedev. Online Political Flashmob: the Case of 632305222316434 // Computational mathematics and information technologies, 2019, No 1, pp. 17–28. DOI: 10.23947/2587-8999-2019-1-1-17-28.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Podlipskaia O.G. (2022) Duration of the Public Attention to Terrorist Attacks in the United States: Does It Depend on Political Opinion? Monitoring of Public Opinion: Economic and Social Changes, No 1, pp. 5-21. https://doi.org/10.14515/monitoring.2022.1.2019. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Podlipskaia O.G. (2022) Duration of the Public Attention to Terrorist Attacks in the United States: Does It Depend on Political Opinion? Monitoring of Public Opinion: Economic and Social Changes, No 1, pp. 5-21. https://doi.org/10.14515/monitoring.2022.1.2019. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">A. Akhremenko, A. Petrov. Modeling the Protest-Repression Nexus // Proceedings of the Conference on Modeling and Analysis of Complex Systems and Processes, 2020, pp. 1-11. http://ceur-ws.org/Vol-2795/paper1.pdf</mixed-citation><mixed-citation xml:lang="en">A. Akhremenko, A. Petrov. Modeling the Protest-Repression Nexus // Proceedings of the Conference on Modeling and Analysis of Complex Systems and Processes, 2020, pp. 1-11. http://ceur-ws.org/Vol-2795/paper1.pdf</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Pronchev G.B., Shisharina E.V., Proncheva N.G. Cyber threats for modern Russia in the context of the coronavirus pandemic // Political Science Issues, Vol. 11, pp. 26-34. DOI: 10.35775/PSI.2021.48.1.003.</mixed-citation><mixed-citation xml:lang="en">Pronchev G.B., Shisharina E.V., Proncheva N.G. Cyber threats for modern Russia in the context of the coronavirus pandemic // Political Science Issues, Vol. 11, pp. 26-34. DOI: 10.35775/PSI.2021.48.1.003.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Proncheva, O. A Model of Propaganda Battle with Individuals’ Opinions on Topics Saliency.13th International Conference Management of largescale system development, 2020, pp. 1-4. DOI: 10.1109/MLSD49919.2020.9247796.</mixed-citation><mixed-citation xml:lang="en">Proncheva, O. A Model of Propaganda Battle with Individuals’ Opinions on Topics Saliency.13th International Conference Management of largescale system development, 2020, pp. 1-4. DOI: 10.1109/MLSD49919.2020.9247796.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">A. Petrov, O. Proncheva. Identifying the Topics of Russian Political Talk Shows // Proceedings of the Conference on Modeling and Analysis of Complex Systems and Processes, 2020, pp. 79-86. DOI: 10.6084/m9.figshare.15109338, http://ceur-ws.org/Vol-2795/short1.pdf.</mixed-citation><mixed-citation xml:lang="en">A. Petrov, O. Proncheva. Identifying the Topics of Russian Political Talk Shows // Proceedings of the Conference on Modeling and Analysis of Complex Systems and Processes, 2020, pp. 79-86. DOI: 10.6084/m9.figshare.15109338, http://ceur-ws.org/Vol-2795/short1.pdf.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
