Rodrigo Conde, Franco Robledo, Agustín López de Lacalle
Since the countryside is one of the main drivers of the global economy, it is vital to support its technological development. When a potential investor contemplates agribusiness investments, several alternatives are presented to him, including forestry, livestock raising, and silvopastoralism, which consists of integrating both activities into a single agroforestry system. In this paper, we address the problem of designing a portfolio of agroforestry investments that maximizes economic results. In order to do so, we developed an integer linear programming model, which selects the optimal combination of the three aforementioned activities for a zoned field. This model was created from a national perspective, considering elements specific to the Uruguayan reality. Additionally, we produced a model implementation utilizing cutting-edge software such as AMPL and CPLEX. This solution was empirically validated using a battery of 56 test cases, based on actual data gathered from multiple sources.
{"title":"Silvopastoral and agroforestry systems: An integer linear programming model for investment decisions","authors":"Rodrigo Conde, Franco Robledo, Agustín López de Lacalle","doi":"10.3934/jdg.2023013","DOIUrl":"https://doi.org/10.3934/jdg.2023013","url":null,"abstract":"Since the countryside is one of the main drivers of the global economy, it is vital to support its technological development. When a potential investor contemplates agribusiness investments, several alternatives are presented to him, including forestry, livestock raising, and silvopastoralism, which consists of integrating both activities into a single agroforestry system. In this paper, we address the problem of designing a portfolio of agroforestry investments that maximizes economic results. In order to do so, we developed an integer linear programming model, which selects the optimal combination of the three aforementioned activities for a zoned field. This model was created from a national perspective, considering elements specific to the Uruguayan reality. Additionally, we produced a model implementation utilizing cutting-edge software such as AMPL and CPLEX. This solution was empirically validated using a battery of 56 test cases, based on actual data gathered from multiple sources.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135594709","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}
Today, tax is the most important and at the same time the most stable source of income for countries and its significant importance indicates that the higher the proportion of taxes to government expenses, the more it remarkably hinders the occurrence of undesirable economic effects. This article addresses the modeling of the game between taxpayers and tax investigating groups in two scenarios - willing and unwilling to collusion - and analyzes the results for each of the two players. Among the most important findings are the inverse relationship between the diagnostic tax function of each group of taxpayers and their declared taxes of the same type, as well as the direct correlation between the diagnostic tax function and the declared taxes of the other group of taxpayers. Furthermore, declared taxes have a direct relationship with tax fine rates, the relevant tax investigating group for the taxpayer, and an inverse correlation with the ratio of the other tax investigating group. If the number of taxpayers increases, the declared taxes of both the willing and unwilling to collusion groups will be equal. The income function of the tax affairs organization is also decreasing toward to the number of willing to collusion taxpayers, the investigating group willing to collusion, and undesirability and increasing toward to the investigating group unwilling to collusion and the increasing number of taxpayers. Finally, it is suggested that the tax affairs organization and relevant tax authorities use the results of this research to neutralize collusion and identify factors influencing diagnostic and declared taxes.
{"title":"Game modeling of collusion and influential factors under uniform taxpayer distribution","authors":"Salah Salimian, Mohammad Hadi Sobhanian","doi":"10.3934/jdg.2023016","DOIUrl":"https://doi.org/10.3934/jdg.2023016","url":null,"abstract":"Today, tax is the most important and at the same time the most stable source of income for countries and its significant importance indicates that the higher the proportion of taxes to government expenses, the more it remarkably hinders the occurrence of undesirable economic effects. This article addresses the modeling of the game between taxpayers and tax investigating groups in two scenarios - willing and unwilling to collusion - and analyzes the results for each of the two players. Among the most important findings are the inverse relationship between the diagnostic tax function of each group of taxpayers and their declared taxes of the same type, as well as the direct correlation between the diagnostic tax function and the declared taxes of the other group of taxpayers. Furthermore, declared taxes have a direct relationship with tax fine rates, the relevant tax investigating group for the taxpayer, and an inverse correlation with the ratio of the other tax investigating group. If the number of taxpayers increases, the declared taxes of both the willing and unwilling to collusion groups will be equal. The income function of the tax affairs organization is also decreasing toward to the number of willing to collusion taxpayers, the investigating group willing to collusion, and undesirability and increasing toward to the investigating group unwilling to collusion and the increasing number of taxpayers. Finally, it is suggested that the tax affairs organization and relevant tax authorities use the results of this research to neutralize collusion and identify factors influencing diagnostic and declared taxes.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136053980","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":"Understanding the role of the environment on the dynamic of tourism and economic growth: New assumptions in terms of time and population growth rate","authors":"Pilar Lorenzo, Martín Olivera","doi":"10.3934/jdg.2023007","DOIUrl":"https://doi.org/10.3934/jdg.2023007","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"10 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75550073","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 present paper aims to study a robust-entropic optimal control problem arising in a general stochastic factor model framework. To be more precise, we consider a portfolio manager who has the possibility to invest part of her wealth in a financial market consisting of two assets: a risk-free asset (e.g., bank account) and a risky one (e.g., stock or index). Furthermore, it is assumed that the dynamics of the risky asset depend on some external stochastic factor. Model uncertainty aspects are introduced as the portfolio manager does not fully trust the model she faces, hence she decides to make her decision robust. By employing a mixture of robust control and dynamic programming techniques within a very general framework, we are able to characterize the optimal robust value function and the feedback control law by solving an expected utility maximization problem. In the special case the portfolio manager operates under the exponential utility function, we provide closed form solutions for the optimal investment decision and the optimal value function for an interesting example arising in finance. Finally, we present a numerical example of our results with special focus given on the impact of robustness on the optimal decision of the portfolio manager.
{"title":"Optimal investment in a general stochastic factor framework under model uncertainty","authors":"Ioannis Baltas","doi":"10.3934/jdg.2023011","DOIUrl":"https://doi.org/10.3934/jdg.2023011","url":null,"abstract":"The present paper aims to study a robust-entropic optimal control problem arising in a general stochastic factor model framework. To be more precise, we consider a portfolio manager who has the possibility to invest part of her wealth in a financial market consisting of two assets: a risk-free asset (e.g., bank account) and a risky one (e.g., stock or index). Furthermore, it is assumed that the dynamics of the risky asset depend on some external stochastic factor. Model uncertainty aspects are introduced as the portfolio manager does not fully trust the model she faces, hence she decides to make her decision robust. By employing a mixture of robust control and dynamic programming techniques within a very general framework, we are able to characterize the optimal robust value function and the feedback control law by solving an expected utility maximization problem. In the special case the portfolio manager operates under the exponential utility function, we provide closed form solutions for the optimal investment decision and the optimal value function for an interesting example arising in finance. Finally, we present a numerical example of our results with special focus given on the impact of robustness on the optimal decision of the portfolio manager.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135494622","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":"Two characterizations of cost share equilibria","authors":"M. Graziano, Marialaura Pesce, M. Romaniello","doi":"10.3934/jdg.2023002","DOIUrl":"https://doi.org/10.3934/jdg.2023002","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"31 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82549551","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":"Producer behavior with rules of origin","authors":"Laura Díaz, J. Sempere","doi":"10.3934/jdg.2023006","DOIUrl":"https://doi.org/10.3934/jdg.2023006","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"81 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83917648","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}
Leon Petrosyan, David Yeung, Yaroslavna Pankratova
In the paper, a class of cooperative differential games on networks is considered. In such games, the new characteristic function is introduced based on the possibility of stopping interaction by players outside the coalition in each time instant or imposing sanction on players from the coalition. This gives the real possibility for the computation of characteristic function. Thus, the characteristic function is evaluated along the cooperative trajectory. It measures the worth of coalitions under the process of cooperation instead of under minimax confrontation or the Nash non-cooperative stance. The approach essentially simplifies the construction of the characteristic function and cooperative solutions such as the Shapley value, Core, $ tau $-value and others. Also, it is proved that the proposed characteristic function is convex, time consistent, and as a result, the Shapley value belongs to the Core and is time consistent. Also, a modification of the dynamic game on networks, namely, dynamic network game with partner sets is considered. In this case, payoffs of a given player depend on his actions and the actions of the players from his partner set. Using previous ideas, the special type of characteristic function is introduced, and cooperative solutions are proposed.
本文研究了一类网络上的合作微分对策。在这种游戏中，新的特征功能是基于在每个时刻停止联盟外玩家的互动或对联盟内玩家施加制裁的可能性而引入的。这为特征函数的计算提供了真正的可能性。因此，沿合作轨迹对特征函数进行评估。它衡量的是联盟在合作过程中的价值，而不是在极大极小对抗或纳什非合作立场下的价值。该方法本质上简化了特征函数和Shapley值、Core、$ tau $-value等合作解的构造。并证明了所提特征函数是凸的，时间一致的，因此Shapley值属于Core值，是时间一致的。同时，考虑了网络上动态博弈的一种修正，即具有伙伴集的动态网络博弈。在这种情况下，给定参与者的收益取决于他的行为和他的伙伴的行为。利用前人的思想，引入了特殊类型的特征函数，并提出了合作解。
{"title":"Characteristic functions in cooperative differential games on networks","authors":"Leon Petrosyan, David Yeung, Yaroslavna Pankratova","doi":"10.3934/jdg.2023017","DOIUrl":"https://doi.org/10.3934/jdg.2023017","url":null,"abstract":"In the paper, a class of cooperative differential games on networks is considered. In such games, the new characteristic function is introduced based on the possibility of stopping interaction by players outside the coalition in each time instant or imposing sanction on players from the coalition. This gives the real possibility for the computation of characteristic function. Thus, the characteristic function is evaluated along the cooperative trajectory. It measures the worth of coalitions under the process of cooperation instead of under minimax confrontation or the Nash non-cooperative stance. The approach essentially simplifies the construction of the characteristic function and cooperative solutions such as the Shapley value, Core, $ tau $-value and others. Also, it is proved that the proposed characteristic function is convex, time consistent, and as a result, the Shapley value belongs to the Core and is time consistent. Also, a modification of the dynamic game on networks, namely, dynamic network game with partner sets is considered. In this case, payoffs of a given player depend on his actions and the actions of the players from his partner set. Using previous ideas, the special type of characteristic function is introduced, and cooperative solutions are proposed.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009466","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}
Today, financing the government's expenses through taxes is the main and, at the same time, the most stable method, with the least negative economic consequences, stabilizing the economy by adopting optimal policies in recession and inflation conditions. The costs for the government have increased due to the extent of the government's obligations in the economic and social fields, requiring the implementation of ways to increase tax revenues and obtain resources to cover these costs. This paper deals with modeling the game between the taxpayers and the tax administration to achieve the factors affecting the optimal performance tax rate and determine the optimal performance tax rate. Assuming that the income of the tax affairs organization (government) is distributed triangularly in the interval [0, 1], and the quality of the investigating group is not known to the taxpayers, the proposed game is solved, and theorems are presented. The results showed that the income of the tax affairs organization had an inverse relationship with investigation costs and a direct relationship with the fines received from the taxpayers. Also, under certain conditions, the income of the tax affairs organization increases with the increase in the quality of the assessment groups. Finally, there was an inverse relationship between the optimal tax rate and the variables of investigating quality and diagnostic tax.
{"title":"Salah-Mohammad triangular distribution Curve is an Alternative to the Laffer curve","authors":"Salah Salimian, Mohammad Hadi Sobhanian","doi":"10.3934/jdg.2023021","DOIUrl":"https://doi.org/10.3934/jdg.2023021","url":null,"abstract":"Today, financing the government's expenses through taxes is the main and, at the same time, the most stable method, with the least negative economic consequences, stabilizing the economy by adopting optimal policies in recession and inflation conditions. The costs for the government have increased due to the extent of the government's obligations in the economic and social fields, requiring the implementation of ways to increase tax revenues and obtain resources to cover these costs. This paper deals with modeling the game between the taxpayers and the tax administration to achieve the factors affecting the optimal performance tax rate and determine the optimal performance tax rate. Assuming that the income of the tax affairs organization (government) is distributed triangularly in the interval [0, 1], and the quality of the investigating group is not known to the taxpayers, the proposed game is solved, and theorems are presented. The results showed that the income of the tax affairs organization had an inverse relationship with investigation costs and a direct relationship with the fines received from the taxpayers. Also, under certain conditions, the income of the tax affairs organization increases with the increase in the quality of the assessment groups. Finally, there was an inverse relationship between the optimal tax rate and the variables of investigating quality and diagnostic tax.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135263008","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":"Can the indifferent population affect the spread of rumors?","authors":"E. Accinelli, L. Quintas, H. Muñiz, Jorge Zazueta","doi":"10.3934/jdg.2023005","DOIUrl":"https://doi.org/10.3934/jdg.2023005","url":null,"abstract":"","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"66 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74947327","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}
Justina Gianatti, Francisco J. Silva, Ahmad Zorkot
We consider a deterministic mean field game problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect to the state variable. In this framework, we construct a mean field game problem in discrete time and finite state space that approximates equilibria of the original game. Two numerical examples, solved with the fictitious play method, are presented.
{"title":"Approximation of deterministic mean field games under polynomial growth conditions on the data","authors":"Justina Gianatti, Francisco J. Silva, Ahmad Zorkot","doi":"10.3934/jdg.2023018","DOIUrl":"https://doi.org/10.3934/jdg.2023018","url":null,"abstract":"We consider a deterministic mean field game problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect to the state variable. In this framework, we construct a mean field game problem in discrete time and finite state space that approximates equilibria of the original game. Two numerical examples, solved with the fictitious play method, are presented.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135010490","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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