A generalized $N$-sided die is a random variable $D$ on a sample space of $N$ equally likely outcomes taking values in the set of positive integers. We say of independent $N$ sided dice $D_i, D_j$ that $D_i$ beats $D_j$, written $D_i to D_j$, if $Prob(D_i > D_j) > frac{1}{2} $. A collection of dice ${ D_i : i = 1, dots, n }$ models a tournament on the set $[n] = { 1, 2, dots, n }$, i.e. a complete digraph with $n$ vertices, when $D_i to D_j$ if and only if $i to j$ in the tournament. By using $n$-fold partitions of the set $[Nn] $ with each set of size $N$ we can model an arbitrary tournament on $[n]$. A bound on the required size of $N$ is obtained by examples with $N = 3^{n-2}$.
{"title":"Generalized intransitive dice II: Partition constructions","authors":"E. Akin, Julia Saccamano","doi":"10.3934/JDG.2021005","DOIUrl":"https://doi.org/10.3934/JDG.2021005","url":null,"abstract":"A generalized $N$-sided die is a random variable $D$ on a sample space of $N$ equally likely outcomes taking values in the set of positive integers. We say of independent $N$ sided dice $D_i, D_j$ that $D_i$ beats $D_j$, written $D_i to D_j$, if $Prob(D_i > D_j) > frac{1}{2} $. A collection of dice ${ D_i : i = 1, dots, n }$ models a tournament on the set $[n] = { 1, 2, dots, n }$, i.e. a complete digraph with $n$ vertices, when $D_i to D_j$ if and only if $i to j$ in the tournament. By using $n$-fold partitions of the set $[Nn] $ with each set of size $N$ we can model an arbitrary tournament on $[n]$. A bound on the required size of $N$ is obtained by examples with $N = 3^{n-2}$.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45671766","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}
This paper analyzes a group of nine Latin American currencies with the aim of identifying clusters of exchange rates with similar co-movements. In this work the study of currency relationships is formulated as a network problem, where each currency is represented as a node and the relationship between each pair of currencies as a link. The paper combines two methods, Symbolic Time Series Analysis (STSA) and a clustering method based on the Minimal Spanning Tree (MST), from which we obtain a Hierarchical Tree (HT). Symbolic Time Series Analysis consists in the transformation of a given time series into a symbolic sequence with the aim of identifying patterns in the set of data. The Minimal Spanning Tree condenses the core information on the global structure of the network and its main advantage is that it greatly simplifies comparisons by dramatically reducing the number of elements that must be compared. We identify two main clusters in the currency network, as well as specific currencies that function as transmission channels between clusters. Using data regarding the degree of financial liberalization, as well as the distinction between inflation targeting (IT) and non-IT countries, the analysis suggests that the obtained taxonomy is economically relevant.
{"title":"An application of minimal spanning trees and hierarchical trees to the study of Latin American exchange rates","authors":"E. Limas","doi":"10.3934/JDG.2019010","DOIUrl":"https://doi.org/10.3934/JDG.2019010","url":null,"abstract":"This paper analyzes a group of nine Latin American currencies with the aim of identifying clusters of exchange rates with similar co-movements. In this work the study of currency relationships is formulated as a network problem, where each currency is represented as a node and the relationship between each pair of currencies as a link. The paper combines two methods, Symbolic Time Series Analysis (STSA) and a clustering method based on the Minimal Spanning Tree (MST), from which we obtain a Hierarchical Tree (HT). Symbolic Time Series Analysis consists in the transformation of a given time series into a symbolic sequence with the aim of identifying patterns in the set of data. The Minimal Spanning Tree condenses the core information on the global structure of the network and its main advantage is that it greatly simplifies comparisons by dramatically reducing the number of elements that must be compared. We identify two main clusters in the currency network, as well as specific currencies that function as transmission channels between clusters. Using data regarding the degree of financial liberalization, as well as the distinction between inflation targeting (IT) and non-IT countries, the analysis suggests that the obtained taxonomy is economically relevant.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44423211","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}
Extensive livestock farmers have to manage climate risk. Therefore, there is a need to generate quantitative tools to evaluate the biophysical and economic impacts on extensive farming based on native grasslands. We present an ecological model based on the predator-prey approach, used to simulate the effect of forage deficiency on the farm's economic performance. Different scenarios of animal stocking rate and carrying capacity of grassland are considered to assess the impact of forage deficiency in spring. Results suggest a cubic response of Gross product per hectare as function of Gross margin, according Mott's theoretical model for meat production on grassland systems in response to stocking rate. The maximum value of this cubic response function strongly depends on the initial grass height and climate scenarios. The initial grass height is critical to maximize secondary productivity and farm economic results. Scenarios including grass reserves can buffer the deficiency on grass growth rates and pasture offer, as occurs in drought periods at the time when farmers try to make animals gain liveweight. Our analysis reinforces the usefulness of forage assignment adjustment by modulating stocking rate to improve liveweight gain and economic results under climate change conditions.
{"title":"AN application of a dynamical model with ecological predator-prey approach to extensive livestock farming in uruguay: Economical assessment on forage deficiency","authors":"F. Dieguez, H. Fort","doi":"10.3934/JDG.2019009","DOIUrl":"https://doi.org/10.3934/JDG.2019009","url":null,"abstract":"Extensive livestock farmers have to manage climate risk. Therefore, there is a need to generate quantitative tools to evaluate the biophysical and economic impacts on extensive farming based on native grasslands. We present an ecological model based on the predator-prey approach, used to simulate the effect of forage deficiency on the farm's economic performance. Different scenarios of animal stocking rate and carrying capacity of grassland are considered to assess the impact of forage deficiency in spring. Results suggest a cubic response of Gross product per hectare as function of Gross margin, according Mott's theoretical model for meat production on grassland systems in response to stocking rate. The maximum value of this cubic response function strongly depends on the initial grass height and climate scenarios. The initial grass height is critical to maximize secondary productivity and farm economic results. Scenarios including grass reserves can buffer the deficiency on grass growth rates and pasture offer, as occurs in drought periods at the time when farmers try to make animals gain liveweight. Our analysis reinforces the usefulness of forage assignment adjustment by modulating stocking rate to improve liveweight gain and economic results under climate change conditions.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48884933","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 apply the skill-relatedness (SR) indicator measure for the analysis of labor flow dynamics in Argentina, and compare it with the original flows in order to differentiate the type of information that each of these techniques offers for characterizing the productive system based on the dynamics of private formal employment. On the other hand, given the size and complexity of the obtained networks, it is interesting to explore the biases introduced by different methods of network reduction in the derived structures as well as to characterize the obtained industrial spaces.
{"title":"Labor mobility and industrial space in Argentina","authors":"Sergio Andrés De Raco, Viktoriya Semeshenko","doi":"10.3934/JDG.2019008","DOIUrl":"https://doi.org/10.3934/JDG.2019008","url":null,"abstract":"In this paper, we apply the skill-relatedness (SR) indicator measure for the analysis of labor flow dynamics in Argentina, and compare it with the original flows in order to differentiate the type of information that each of these techniques offers for characterizing the productive system based on the dynamics of private formal employment. On the other hand, given the size and complexity of the obtained networks, it is interesting to explore the biases introduced by different methods of network reduction in the derived structures as well as to characterize the obtained industrial spaces.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45523689","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}
Economic evolution is said to occur when economic structures change. That is, when the institutional and/or technological rules of the society are replaced by new ones. As with evolutionary phenomena in other fields it is rather impossible to predict such changes. In this paper we present a simple model of evolutionary changes caused by uncertainty about the possible future states of the economy. Agents faced with uncertainty behave in such a way as to either lead the economy to another state or adjust themselves to the newly known environment. In either case, the change involves the modification of one or more fundamental parameters of the economy. Such modification is what we call an evolutionary change. We prove an impossibility result, stating that there is no way of coordinating those adjustments as to make true any given forecast. Moreover, we show that uncertainty about the future is a real source of novelty.
{"title":"Economic evolution and uncertainty: Transitions and structural changes","authors":"Silvia London, F. Tohmé","doi":"10.3934/JDG.2019011","DOIUrl":"https://doi.org/10.3934/JDG.2019011","url":null,"abstract":"Economic evolution is said to occur when economic structures change. That is, when the institutional and/or technological rules of the society are replaced by new ones. As with evolutionary phenomena in other fields it is rather impossible to predict such changes. In this paper we present a simple model of evolutionary changes caused by uncertainty about the possible future states of the economy. Agents faced with uncertainty behave in such a way as to either lead the economy to another state or adjust themselves to the newly known environment. In either case, the change involves the modification of one or more fundamental parameters of the economy. Such modification is what we call an evolutionary change. We prove an impossibility result, stating that there is no way of coordinating those adjustments as to make true any given forecast. Moreover, we show that uncertainty about the future is a real source of novelty.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44829741","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}
Martha G. Alatriste-Contreras, J. Brida, M. P. Anyul
Economic systems have evolved through time thereby changing the structure that characterizes them. These changes respond to technological changes that transform economies into highly interconnected systems. The modifications in the norms that guide the behaviour of organizations and, therefore the functioning of the economy, are a first case of this transformation. The industrialization process, through the incorporation of increasing returns to scale in different sectors, and the introduction of service activities are other examples. Another form to represent structural change is the change of the values of the variables that characterize the state space of an economic system. This research article is an effort to put together and compare, from the complexity approach, different approaches for structural change and dynamics of economic systems. We start by briefly presenting the complexity approach in general and in economics. Then, we put forward three approaches highlighting structural change.
{"title":"Structural change and economic dynamics: Rethinking from the complexity approach","authors":"Martha G. Alatriste-Contreras, J. Brida, M. P. Anyul","doi":"10.3934/JDG.2019007","DOIUrl":"https://doi.org/10.3934/JDG.2019007","url":null,"abstract":"Economic systems have evolved through time thereby changing the structure that characterizes them. These changes respond to technological changes that transform economies into highly interconnected systems. The modifications in the norms that guide the behaviour of organizations and, therefore the functioning of the economy, are a first case of this transformation. The industrialization process, through the incorporation of increasing returns to scale in different sectors, and the introduction of service activities are other examples. Another form to represent structural change is the change of the values of the variables that characterize the state space of an economic system. This research article is an effort to put together and compare, from the complexity approach, different approaches for structural change and dynamics of economic systems. We start by briefly presenting the complexity approach in general and in economics. Then, we put forward three approaches highlighting structural change.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41329105","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}
L. Rodríguez-gallego, Antonella Barletta Carolina Cabrera, C. Kruk, M. Nin, Antonio Mauttone
Biodiversity conservation and ecosystem services provision can compete with other land uses due to its incompatibility with many productive activities. The need for multifunctional landscapes that simultaneously provide food security, maintenance of ecological functions and fulfill welfare requirements is evident. Multi-objective optimization procedures can select between different land uses in each parcel of the territory, simultaneously satisfying contrasting objectives. Each solution (a map) represents a spatial configuration of land uses, generating spatial alternatives and offering flexibility to conduct discussions among social actors. In order to prevent eutrophication we developed a methodological approach for planning land-use transformations in productive territories, considering ecological processes from the beginning. A two-objective approach was used to allocate different land uses in the most suitable sites (objective one) that simultaneously minimize nutrients exportation (objective two). The land uses allocation was Pareto optimal and was conducted by integer linear programming. According to the relative importance given to each objective, two types of land use allocation were obtained, one dominated by agriculture but where a threshold of phosphorus load was exceeded, and another one where conservation and livestock ranching on natural grasslands prevailed and the phosphorus load decreased dramatically. This spatially explicit tool helps decision makers to design multifunctional landscapes for sustainable development and promote social discussions.
{"title":"Establishing limits to agriculture and afforestation: A GIS based multi-objective approach to prevent algal blooms in a coastal lagoon","authors":"L. Rodríguez-gallego, Antonella Barletta Carolina Cabrera, C. Kruk, M. Nin, Antonio Mauttone","doi":"10.3934/JDG.2019012","DOIUrl":"https://doi.org/10.3934/JDG.2019012","url":null,"abstract":"Biodiversity conservation and ecosystem services provision can compete with other land uses due to its incompatibility with many productive activities. The need for multifunctional landscapes that simultaneously provide food security, maintenance of ecological functions and fulfill welfare requirements is evident. Multi-objective optimization procedures can select between different land uses in each parcel of the territory, simultaneously satisfying contrasting objectives. Each solution (a map) represents a spatial configuration of land uses, generating spatial alternatives and offering flexibility to conduct discussions among social actors. In order to prevent eutrophication we developed a methodological approach for planning land-use transformations in productive territories, considering ecological processes from the beginning. A two-objective approach was used to allocate different land uses in the most suitable sites (objective one) that simultaneously minimize nutrients exportation (objective two). The land uses allocation was Pareto optimal and was conducted by integer linear programming. According to the relative importance given to each objective, two types of land use allocation were obtained, one dominated by agriculture but where a threshold of phosphorus load was exceeded, and another one where conservation and livestock ranching on natural grasslands prevailed and the phosphorus load decreased dramatically. This spatially explicit tool helps decision makers to design multifunctional landscapes for sustainable development and promote social discussions.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47582795","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}
E. Accinelli, E. Carrera, Laura Policardo, Osvaldo Salas
In this paper, we consider a two-country and two-sector economy, where firms can choose to be innovative or not innovative, and workers to be skilled or unskilled. Using a dynamic game, we argue that exploiting the comparative advantages a country has in producing goods that use the most abundant factor of production, free mobility of capital and labor is beneficial for economic growth. However, if a country has a comparative advantage in a sector that uses intensely unskilled labor (which is the case of several underdeveloped economies), a poverty trap may arise. For this reason we argue that national Governments must ensure the technological development to improve competitiveness and therefore a social optimal use of the comparative advantages.
{"title":"Free mobility of capital and Labor force in a two-country model: The dynamic game for growth","authors":"E. Accinelli, E. Carrera, Laura Policardo, Osvaldo Salas","doi":"10.3934/JDG.2019013","DOIUrl":"https://doi.org/10.3934/JDG.2019013","url":null,"abstract":"In this paper, we consider a two-country and two-sector economy, where firms can choose to be innovative or not innovative, and workers to be skilled or unskilled. Using a dynamic game, we argue that exploiting the comparative advantages a country has in producing goods that use the most abundant factor of production, free mobility of capital and labor is beneficial for economic growth. However, if a country has a comparative advantage in a sector that uses intensely unskilled labor (which is the case of several underdeveloped economies), a poverty trap may arise. For this reason we argue that national Governments must ensure the technological development to improve competitiveness and therefore a social optimal use of the comparative advantages.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42600568","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}
M. T. V. Martínez-Palacios, A. Hernández-del-Valle, Ambrosio Ortiz-Ramírez
In this work, through stochastic optimal control in continuous time the optimal decision making in consumption and investment is modeled by a rational economic agent, representative of an economy, who is a consumer and an investor adverse to risk; this in a finite time horizon of stochastic length. The assumptions of the model are: a consumption function of HARA type, a representative company that has a stochastic production process, the agent invests in a stock and an American-style Asian put option with floating strike equal to the geometric average subscribed on the stock, both modeled by controlled Markovian processes; as well as the investment of a principal in a bank account. The model is solved with dynamic programming in continuous time, particularly the Hamilton-Jacobi-Bellman PDE is obtained, and a function in separable variables is proposed as a solution to set the optimal trajectories of consumption and investment. In the solution analysis is determined: in equilibrium, the process of short interest rate that is driven by a square root process with reversion to the mean; and through a system of differential equations of risk premiums, a PDE is deduced equivalent to the Black-Scholes-Merton but to value an American-style Asian put option.
{"title":"On the pricing of Asian options with geometric average of American type with stochastic interest rate: A stochastic optimal control approach","authors":"M. T. V. Martínez-Palacios, A. Hernández-del-Valle, Ambrosio Ortiz-Ramírez","doi":"10.3934/jdg.2019004","DOIUrl":"https://doi.org/10.3934/jdg.2019004","url":null,"abstract":"In this work, through stochastic optimal control in continuous time the optimal decision making in consumption and investment is modeled by a rational economic agent, representative of an economy, who is a consumer and an investor adverse to risk; this in a finite time horizon of stochastic length. The assumptions of the model are: a consumption function of HARA type, a representative company that has a stochastic production process, the agent invests in a stock and an American-style Asian put option with floating strike equal to the geometric average subscribed on the stock, both modeled by controlled Markovian processes; as well as the investment of a principal in a bank account. The model is solved with dynamic programming in continuous time, particularly the Hamilton-Jacobi-Bellman PDE is obtained, and a function in separable variables is proposed as a solution to set the optimal trajectories of consumption and investment. In the solution analysis is determined: in equilibrium, the process of short interest rate that is driven by a square root process with reversion to the mean; and through a system of differential equations of risk premiums, a PDE is deduced equivalent to the Black-Scholes-Merton but to value an American-style Asian put option.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47502863","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}
A generalized $N$-sided die is a random variable $D$ on a sample space of $N$ equally likely outcomes taking values in the set of positive integers. We say of independent $N$ sided dice $D_i, D_j$ that $D_i$ beats $D_j$, written $D_i to D_j$, if $Prob(D_i > D_j) > frac{1}{2} $. Examples are known of intransitive $6$-sided dice, i.e. $D_1 to D_2 to D_3$ but $D_3 to D_1$. A tournament of size $n$ is a choice of direction $i to j$ for each edge of the complete graph on $n$ vertices. We show that if $R$ is tournament on the set ${ 1, dots, n }$, then for sufficiently large $N$ there exist sets of independent $N$-sided dice ${ D_1, dots, D_n }$ such that $D_i to D_j$ if and only if $i to j$ in $R$.
{"title":"Generalized intransitive dice: Mimicking an arbitrary tournament","authors":"E. Akin","doi":"10.3934/jdg.2020030","DOIUrl":"https://doi.org/10.3934/jdg.2020030","url":null,"abstract":"A generalized $N$-sided die is a random variable $D$ on a sample space of $N$ equally likely outcomes taking values in the set of positive integers. We say of independent $N$ sided dice $D_i, D_j$ that $D_i$ beats $D_j$, written $D_i to D_j$, if $Prob(D_i > D_j) > frac{1}{2} $. Examples are known of intransitive $6$-sided dice, i.e. $D_1 to D_2 to D_3$ but $D_3 to D_1$. A tournament of size $n$ is a choice of direction $i to j$ for each edge of the complete graph on $n$ vertices. We show that if $R$ is tournament on the set ${ 1, dots, n }$, then for sufficiently large $N$ there exist sets of independent $N$-sided dice ${ D_1, dots, D_n }$ such that $D_i to D_j$ if and only if $i to j$ in $R$.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47612687","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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