This paper analyzes the impact on the spread of the COVID-19 virus of making virtual the educational system in the Region of Aysen in Chile. The analyzes is made through a mix of agent-based modelling and microsim-ulation techniques, using multiple sources of administrative and census data. The behavior of 103,000 habitants of the region is modeled during each one of the seven days of the week, for 10 weeks. The diffusion of the virus is mod-eled as consequence of the social interaction of the individuals in five different environments: home, the transportation system, at work, the educational sys-tem and in places of entertainment. The results show that the closure of the educational system is important to flatten the curve of contagious. In a world where people don't do social distancing, it could lower R0 by one unit.
{"title":"An agent-based and microsimulated model of the epidemiology impact of closure of schools during the COVID-19 pandemic in the region of Aysen in Chile","authors":"Gabriel Brida, Nicolás Garrido","doi":"10.3934/jdg.2023003","DOIUrl":"https://doi.org/10.3934/jdg.2023003","url":null,"abstract":"This paper analyzes the impact on the spread of the COVID-19 virus of making virtual the educational system in the Region of Aysen in Chile. The analyzes is made through a mix of agent-based modelling and microsim-ulation techniques, using multiple sources of administrative and census data. The behavior of 103,000 habitants of the region is modeled during each one of the seven days of the week, for 10 weeks. The diffusion of the virus is mod-eled as consequence of the social interaction of the individuals in five different environments: home, the transportation system, at work, the educational sys-tem and in places of entertainment. The results show that the closure of the educational system is important to flatten the curve of contagious. In a world where people don't do social distancing, it could lower R0 by one unit.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83127761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider games of two-players with utility functions which are not necessarily linear on the product of convex and compact intervals of begin{document}$ mathcal{R}^2 $end{document}. An issue is how far an analogy can be drawn with two-player, two-strategy matrix games with linear utility functions, where [0, 1] registers probabilities and equilibria are at the intersection of reaction functions. Now, the idea of begin{document}$ delta $end{document} functions is exploited to construct mixed strategies to look for Nash equilibria (NE). "Reaction" functions are constructed and results are obtained graphically. They are related to topological theorems on NE. The games chosen make specific points in relation to existence conditions and properties of solutions. It is a distinguishing feature that an interval [a, b] now registers both pure and mixed strategies. For NE a choice has to be justified. Also "reaction" functions are more complicated and their intersection does not guarantee an equilibrium.
We consider games of two-players with utility functions which are not necessarily linear on the product of convex and compact intervals of begin{document}$ mathcal{R}^2 $end{document}. An issue is how far an analogy can be drawn with two-player, two-strategy matrix games with linear utility functions, where [0, 1] registers probabilities and equilibria are at the intersection of reaction functions. Now, the idea of begin{document}$ delta $end{document} functions is exploited to construct mixed strategies to look for Nash equilibria (NE). "Reaction" functions are constructed and results are obtained graphically. They are related to topological theorems on NE. The games chosen make specific points in relation to existence conditions and properties of solutions. It is a distinguishing feature that an interval [a, b] now registers both pure and mixed strategies. For NE a choice has to be justified. Also "reaction" functions are more complicated and their intersection does not guarantee an equilibrium.
{"title":"On two-player games with pure strategies on intervals $ [a, ; b] $ and comparisons with the two-player, two-strategy matrix case","authors":"Zahra Gambarova, D. Glycopantis","doi":"10.3934/jdg.2022015","DOIUrl":"https://doi.org/10.3934/jdg.2022015","url":null,"abstract":"<p style='text-indent:20px;'>We consider games of two-players with utility functions which are not necessarily linear on the product of convex and compact intervals of <inline-formula><tex-math id=\"M2\">begin{document}$ mathcal{R}^2 $end{document}</tex-math></inline-formula>. An issue is how far an analogy can be drawn with two-player, two-strategy matrix games with linear utility functions, where [0, 1] registers probabilities and equilibria are at the intersection of reaction functions. Now, the idea of <inline-formula><tex-math id=\"M3\">begin{document}$ delta $end{document}</tex-math></inline-formula> functions is exploited to construct mixed strategies to look for Nash equilibria (NE). \"Reaction\" functions are constructed and results are obtained graphically. They are related to topological theorems on NE. The games chosen make specific points in relation to existence conditions and properties of solutions. It is a distinguishing feature that an interval [a, b] now registers both pure and mixed strategies. For NE a choice has to be justified. Also \"reaction\" functions are more complicated and their intersection does not guarantee an equilibrium.</p>","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"27 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90480883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Implicit coordination in an $ n $-player target selection game","authors":"S. Patek","doi":"10.3934/jdg.2022027","DOIUrl":"https://doi.org/10.3934/jdg.2022027","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"14 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85159429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The game-theoretical modelling of a dynamically evolving network: Revisiting the target sequence 111","authors":"","doi":"10.3934/jdg.2022026","DOIUrl":"https://doi.org/10.3934/jdg.2022026","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"121 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85704220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Early warning indicators of epidemics on a coupled behaviour-disease model with vaccine hesitance and incomplete data","authors":"Brendon Phillips, C. Bauch","doi":"10.3934/jdg.2022024","DOIUrl":"https://doi.org/10.3934/jdg.2022024","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"327 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73159437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we study a repeated game and the replicator dynamics to analyze the spread of a rumor in a society formed by two populations. One population is informed about a rumor and communicates the rumor to the other population. According to the preferences of each individual, this rumor is communicated in its original or in a modified form. We analyze the stability of dynamic equilibria. We conclude that there are three possibilities for the spread of a rumor. The rumor may end up being disseminated in its original version or being distorted by the diffusers throughout the society, or a part of the population remains in the long term spreading the rumor in its original form and another in a distorted way.
{"title":"Rumors' spread: A game theoretical approach with the replicator dynamics","authors":"E. Accinelli, L. Quintas, H. Muñiz","doi":"10.3934/jdg.2022020","DOIUrl":"https://doi.org/10.3934/jdg.2022020","url":null,"abstract":"In this paper we study a repeated game and the replicator dynamics to analyze the spread of a rumor in a society formed by two populations. One population is informed about a rumor and communicates the rumor to the other population. According to the preferences of each individual, this rumor is communicated in its original or in a modified form. We analyze the stability of dynamic equilibria. We conclude that there are three possibilities for the spread of a rumor. The rumor may end up being disseminated in its original version or being distorted by the diffusers throughout the society, or a part of the population remains in the long term spreading the rumor in its original form and another in a distorted way.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"12 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87235146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lonnie Turpin, Jr., K. Bruchhaus, Keith R. Credo, Gerard Ornas, Jr.
In this brief work, we study a basic environment consisting of a single receiver taking actions based on information (called signals) from multiple senders. The receiver is a rational Bayesian who uses optimization as a mechanism to convert the signals to actions. The conversions are gambles as the actions must be taken before signal reception. Formal comparisons of differences between the solution sets of both prior and posterior optimization frameworks and their respective probability distributions are given. The difference in probability distributions (denoted by relative entropy) presents a useful tool for modifying the receiver's level of risk. We then construct a simple scenario where the receiver acts as a proxy in a Shapely-Shubik-style game with two agents focusing on different objectives under a common risk level. Acting on their behalf, an envy-free allocation mechanism is presented to simultaneously satisfy each using the asymmetric assignment model when findings show the objectives require identical actions.
{"title":"Relative entropy and envy-free allocation","authors":"Lonnie Turpin, Jr., K. Bruchhaus, Keith R. Credo, Gerard Ornas, Jr.","doi":"10.3934/jdg.2022013","DOIUrl":"https://doi.org/10.3934/jdg.2022013","url":null,"abstract":"In this brief work, we study a basic environment consisting of a single receiver taking actions based on information (called signals) from multiple senders. The receiver is a rational Bayesian who uses optimization as a mechanism to convert the signals to actions. The conversions are gambles as the actions must be taken before signal reception. Formal comparisons of differences between the solution sets of both prior and posterior optimization frameworks and their respective probability distributions are given. The difference in probability distributions (denoted by relative entropy) presents a useful tool for modifying the receiver's level of risk. We then construct a simple scenario where the receiver acts as a proxy in a Shapely-Shubik-style game with two agents focusing on different objectives under a common risk level. Acting on their behalf, an envy-free allocation mechanism is presented to simultaneously satisfy each using the asymmetric assignment model when findings show the objectives require identical actions.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78803175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dai Zusai, Ryoji Sawa, Man-Wah Cheung, R. Lahkar, Jiabin Wu
In this paper, former students of Bill Sandholm provide summaries of Bill's academic contributions as a unifier of evolutionary game theory and also share their personal memories with Bill as a kind, friendly and dedicated mentor. The paper consists on five essays; first on the unification of EGT with the concept of revision protocols and his charming personality, second on stochastic dynamics, third on potential games, fourth on geometric aspects of Bill's analysis, especially on the projection dynamic, and fifth on applications to cultural evolution.
{"title":"Tributes to Bill Sandholm","authors":"Dai Zusai, Ryoji Sawa, Man-Wah Cheung, R. Lahkar, Jiabin Wu","doi":"10.3934/jdg.2022009","DOIUrl":"https://doi.org/10.3934/jdg.2022009","url":null,"abstract":"In this paper, former students of Bill Sandholm provide summaries of Bill's academic contributions as a unifier of evolutionary game theory and also share their personal memories with Bill as a kind, friendly and dedicated mentor. The paper consists on five essays; first on the unification of EGT with the concept of revision protocols and his charming personality, second on stochastic dynamics, third on potential games, fourth on geometric aspects of Bill's analysis, especially on the projection dynamic, and fifth on applications to cultural evolution.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"29 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87683614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We analyze 4 characteristic functions begin{document}$ V^alpha $end{document}, begin{document}$ V^delta $end{document}, begin{document}$ V^zeta $end{document}, and begin{document}$ V^eta $end{document}, and give a necessary condition for these functions to satisfy the relation begin{document}$ V^alpha - V^delta = V^zeta - V^eta $end{document} for all coalitions begin{document}$ S $end{document}. To do so, we define and formally analyze the class of additively separable games. It is shown that many important types of games, both static and dynamic, belong to this class.
We analyze 4 characteristic functions begin{document}$ V^alpha $end{document}, begin{document}$ V^delta $end{document}, begin{document}$ V^zeta $end{document}, and begin{document}$ V^eta $end{document}, and give a necessary condition for these functions to satisfy the relation begin{document}$ V^alpha - V^delta = V^zeta - V^eta $end{document} for all coalitions begin{document}$ S $end{document}. To do so, we define and formally analyze the class of additively separable games. It is shown that many important types of games, both static and dynamic, belong to this class.
{"title":"On the symmetry relation between different characteristic functions for additively separable cooperative games","authors":"E. Gromova, K. Savin","doi":"10.3934/jdg.2022017","DOIUrl":"https://doi.org/10.3934/jdg.2022017","url":null,"abstract":"<p style='text-indent:20px;'>We analyze 4 characteristic functions <inline-formula><tex-math id=\"M1\">begin{document}$ V^alpha $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M2\">begin{document}$ V^delta $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M3\">begin{document}$ V^zeta $end{document}</tex-math></inline-formula>, and <inline-formula><tex-math id=\"M4\">begin{document}$ V^eta $end{document}</tex-math></inline-formula>, and give a necessary condition for these functions to satisfy the relation <inline-formula><tex-math id=\"M5\">begin{document}$ V^alpha - V^delta = V^zeta - V^eta $end{document}</tex-math></inline-formula> for all coalitions <inline-formula><tex-math id=\"M6\">begin{document}$ S $end{document}</tex-math></inline-formula>. To do so, we define and formally analyze the class of additively separable games. It is shown that many important types of games, both static and dynamic, belong to this class.</p>","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"10 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86912567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The stress-strength model is a basic model in the field of reliability, but it still has some obvious limitations in many applications. Therefore, considering different aspects and using different methods to investigate the stress-strength model has been one of the main research directions of reliability. In this paper, we suppose the problem of evaluating reliability considering the stress and strength as dependent variables when the association is modeled by the copula function. By using Monte Carlo simulation, we estimate the reliability measure begin{document}$ R $end{document} for dependent margins by choosing various copulas and known marginal distributions to belong to a specific class of parametric models, here the Dagum family. Finally, the application of the copula-based approach in reliability modelling is illustrated using two medical data sets. The results of these two data sets show the effectiveness of this method in reliability modelling.
The stress-strength model is a basic model in the field of reliability, but it still has some obvious limitations in many applications. Therefore, considering different aspects and using different methods to investigate the stress-strength model has been one of the main research directions of reliability. In this paper, we suppose the problem of evaluating reliability considering the stress and strength as dependent variables when the association is modeled by the copula function. By using Monte Carlo simulation, we estimate the reliability measure begin{document}$ R $end{document} for dependent margins by choosing various copulas and known marginal distributions to belong to a specific class of parametric models, here the Dagum family. Finally, the application of the copula-based approach in reliability modelling is illustrated using two medical data sets. The results of these two data sets show the effectiveness of this method in reliability modelling.
{"title":"Stress-strength reliability with dependent variables based on copula function","authors":"M. B. Ghalibaf","doi":"10.3934/jdg.2022014","DOIUrl":"https://doi.org/10.3934/jdg.2022014","url":null,"abstract":"The stress-strength model is a basic model in the field of reliability, but it still has some obvious limitations in many applications. Therefore, considering different aspects and using different methods to investigate the stress-strength model has been one of the main research directions of reliability. In this paper, we suppose the problem of evaluating reliability considering the stress and strength as dependent variables when the association is modeled by the copula function. By using Monte Carlo simulation, we estimate the reliability measure begin{document}$ R $end{document} for dependent margins by choosing various copulas and known marginal distributions to belong to a specific class of parametric models, here the Dagum family. Finally, the application of the copula-based approach in reliability modelling is illustrated using two medical data sets. The results of these two data sets show the effectiveness of this method in reliability modelling.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"413 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85825683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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