scholarly journals Hierarchical Structures and Leadership Design in Mean-Field-Type Games with Polynomial Cost

Games ◽  
2020 ◽  
Vol 11 (3) ◽  
pp. 30
Author(s):  
Zahrate El Oula Frihi ◽  
Julian Barreiro-Gomez ◽  
Salah Eddine Choutri ◽  
Hamidou Tembine
Keyword(s):  
Control Strategies ◽  
Mean Field ◽  
Single Layer ◽  
Hierarchical Structures ◽  
Hierarchical Systems ◽  
Feedback Form ◽  
Field Type ◽  
The Hierarchical Structure ◽  
Linear State ◽  
Multiple Followers

This article presents a class of hierarchical mean-field-type games with multiple layers and non-quadratic polynomial costs. The decision-makers act in sequential order with informational differences. We first examine the single-layer case where each decision-maker does not have the information about the other control strategies. We derive the Nash mean-field-type equilibrium and cost in a linear state-and-mean-field feedback form by using a partial integro-differential system. Then, we examine the Stackelberg two-layer problem with multiple leaders and multiple followers. Numerical illustrations show that, in the symmetric case, having only one leader is not necessarily optimal for the total sum cost. Having too many leaders may also be suboptimal for the total sum cost. The methodology is extended to multi-level hierarchical systems. It is shown that the order of the play plays a key role in the total performance of the system. We also identify a specific range of parameters for which the Nash equilibrium coincides with the hierarchical solution independently of the number of layers and the order of play. In the heterogeneous case, it is shown that the total cost is significantly affected by the design of the hierarchical structure of the problem.

scholarly journals COVID-19: A Data-Driven Mean-Field-Type Game Perspective

2020 ◽  
Author(s):  
Hamidou Tembine
Keyword(s):  
Mean Field ◽  
Decision Makers ◽  
Data Driven ◽  
Feedback Form ◽  
State Spaces ◽  
Hospital Capacity ◽  
Field Type ◽  
Adjoint Systems ◽  
Continuous State ◽  
Reported Data

In this article, a class of mean-field-type games with discrete-continuous state spaces is considered. We establish Bellman systems which provide sufficiency conditions for mean-field-type equilibria in state-and-mean-field-type feedback form. We then derive unnormalized master adjoint systems (MASS). The methodology is shown to be flexible enough to capture multi-class interaction in epidemic propagation in which multiple authorities are risk-aware atomic decision-makers and individuals are risk-aware non-atomic decision-makers. Based on MASS, we present a data-driven modelling and analytics for mitigating Coronavirus Disease 2019 (COVID-19). The model integrates untested cases, age-structure, decision-making, gender, pre-existing health conditions, location, testing capacity, hospital capacity, mobility map on local areas, in-city, inter-cities, and international. It shown that the data-driven model can capture most of the reported data on COVID-19 on confirmed cases, deaths, recovered, number of testing and number of active cases in 66+ countries. The model also reports non-Gaussianity and non-exponential properties in 15+ countries.

scholarly journals COVID-19: Data-Driven Mean-Field-Type Game Perspective

Games ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 51
Author(s):  
Hamidou Tembine
Keyword(s):  
Mean Field ◽  
Decision Makers ◽  
Data Driven ◽  
Feedback Form ◽  
State Spaces ◽  
Field Type ◽  
Adjoint Systems ◽  
Continuous State ◽  
Non Gaussian ◽  
Reported Data

In this article, a class of mean-field-type games with discrete-continuous state spaces is considered. We establish Bellman systems which provide sufficiency conditions for mean-field-type equilibria in state-and-mean-field-type feedback form. We then derive unnormalized master adjoint systems (MASS). The methodology is shown to be flexible enough to capture multi-class interaction in epidemic propagation in which multiple authorities are risk-aware atomic decision-makers and individuals are risk-aware non-atomic decision-makers. Based on MASS, we present a data-driven modelling and analytics for mitigating Coronavirus Disease 2019 (COVID-19). The model integrates untested cases, age-structure, decision-making, gender, pre-existing health conditions, location, testing capacity, hospital capacity, and a mobility map of local areas, including in-cities, inter-cities, and internationally. It is shown that the data-driven model can capture most of the reported data on COVID-19 on confirmed cases, deaths, recovered, number of testing and number of active cases in 66+ countries. The model also reports non-Gaussian and non-exponential properties in 15+ countries.

Robust H2/H∞Control Strategy for Linear Markovian Jump Systems

2014 ◽  
Vol 525 ◽  
pp. 646-652
Author(s):  
Min Bian ◽  
Qing Yun Guo
Keyword(s):  
Control Strategy ◽  
State Feedback ◽  
Control Strategies ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Bounded Real Lemma ◽  
Finite State ◽  
Linear State ◽  
Feasible Solutions ◽  
Jump Systems

The robust H2/<em>H</em>∞ control strategy for a class of linear continuous-time uncertain systems with randomly jumping parameters is investigated. The transition of the jumping parameters is decided by a finite-state Markov process. The uncertainties are supposed to be norm-bounded. It is desired to design a linear state feedback control strategies such that the closed-loop system satisfies H performance and minimizes the H2 norm of the system. A sufficient condition is first established on the existence of the robust H2/<em>H</em>∞controller bases on the bounded real lemma. Then the corresponding state-feedback law is given in terms of a set of linear matrix inequalities (LMIs). It is showed that this condition is equivalent to the feasible solutions problem of LMI. Furthermore, the control strategy design problem is converted into a convex optimization problem subject to LMI constraints, which can be easily solved by standard numerical software.

Perceiving Hierarchical Structures in Nonrepresentational Paintings

1998 ◽  
Vol 16 (1) ◽  
pp. 59-70 ◽  
Author(s):  
Tsion Avital ◽  
Gerald C. Cupchik
Keyword(s):  
Factor Analysis ◽  
Multidimensional Scaling ◽  
Hierarchical Structure ◽  
Hierarchical Structures ◽  
Exploratory Activity ◽  
Affective Responses ◽  
Hierarchical Complexity ◽  
The Hierarchical Structure ◽  
Relative Separation ◽  
Dimension 2

A series of four experiments were conducted to examine viewer perceptions of three sets of five nonrepresentational paintings. Increased complexity was embedded in the hierarchical structure of each set by carefully selecting colors and ordering them in each successive painting according to certain rules of transformation which created hierarchies. Experiment 1 supported the hypothesis that subjects would discern the hierarchical complexity underlying the sets of paintings. In Experiment 2 viewers rated the paintings on collative (complexity, disorder) and affective (pleasing, interesting, tension, and power) scales, and a factor analysis revealed that affective ratings were tied to complexity (Factor 1) but not to disorder (Factor 2). In Experiment 3, a measure of exploratory activity (free looking time) was correlated with complexity (Factor 1) but not with disorder (Factor 2). Multidimensional scaling was used in Experiment 4 to examine perceptions of the paintings seen in pairs. Dimension 1 contrasted Soft with Hard-Edged paintings, while Dimension 2 reflected the relative separation of figure from ground in these paintings. Together these results show that untrained viewers can discern hierarchical complexity in paintings and that this quality stimulates affective responses and exploratory activity.

Mean-Field-Type Games for Engineers

2021 ◽  
Author(s):  
Julian Barreiro-Gomez ◽  
Hamidou Tembine
Keyword(s):  
Mean Field ◽  
Field Type

Coexistence of cluster structure and mean-field-type structure in medium-weight nuclei

2007 ◽  
Vol 787 (1-4) ◽  
pp. 547-552
Author(s):  
Y. Taniguchi ◽  
M. Kimura ◽  
Y. Kanada-En'yo ◽  
H. Horiuchi
Keyword(s):  
Cluster Structure ◽  
Mean Field ◽  
Type Structure ◽  
Field Type ◽  
Medium Weight
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