# American Institute of Mathematical Sciences

ISSN:
2164-6066

eISSN:
2164-6074

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## Journal of Dynamics and Games

July 2022 , Volume 9 , Issue 3

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2022, 9(3): 229-239 doi: 10.3934/jdg.2022008 +[Abstract](409) +[HTML](139) +[PDF](315.73KB)
Abstract:

Statistical dependence between the GDP growth projection adjustments for the end of 2020 and the health impact of the Covid-19 pandemic is detected and quantified for a broad set of countries. A \begin{document}$\texttt{rate }$\end{document} that captures this health impact for each country is contrasted to the difference in GDP growth projections for the end of 2020 released in two subsequent times: 2019 (pre-pandemic) and early 2020 (post-pandemic). The difference of this two variables exhibited a significant rank correlation with the \begin{document}$\texttt{rate }$\end{document}, and a linear model was successfully fitted, concluding that at the beginning of the pandemic health conditions played a significant role in the GDP projections.

2022, 9(3): 241-252 doi: 10.3934/jdg.2022011 +[Abstract](358) +[HTML](125) +[PDF](346.73KB)
Abstract:

The presence of big data may adversely affect obtaining classification accuracy in many life applications, such as genes dataset, which can contain many unnecessary data in the classification process. In this study, a two-stage mathematical model is proposed through which the features are selected. The first stage relies on the Fuzzy Statistical Dependence (FSD) technique, which is one of the filter techniques, and in the second stage, the Binary Bat Algorithm (BBA) is used, which depends on an appropriate fitness function to select important parameters. The experimental results proved that the proposed algorithm, which we refer to as FSD-BBA, excels over other methods in terms of classification accuracy and the number of influencing genes selected.

2022, 9(3): 253-266 doi: 10.3934/jdg.2022012 +[Abstract](328) +[HTML](104) +[PDF](401.23KB)
Abstract:

In symmetric evolutionary games with continuous strategy spaces, Cressman [6] has proved an interesting stability result for the associated replicator dynamics relating the concepts of neighborhood superiority and neighborhood attracting for polymorphic states with respect to the weak topology. Similar stability results are also established for monomorphic profiles in 2-player asymmetric games [8]. In the present paper, we use the model of asymmetric evolutionary games introduced by Mendoza-Palacios and Hernández-Lerma [17] and obtain a stability result for polymorphic profiles in \begin{document}$n$\end{document}-player asymmetric evolutionary games with continuous action spaces using the concept of neighborhood strong superiority (Definition 2.3). In particular, we prove that neighborhood strong superior polymorphic profiles are neighborhood attracting. It is also shown that a polymorphic neighborhood strong superior profile is in fact a vector of Dirac measures. Moreover, we establish that the notion of neighborhood strong superiority does not imply strong uninvadability and vice-versa.

2022, 9(3): 267-282 doi: 10.3934/jdg.2022013 +[Abstract](319) +[HTML](96) +[PDF](365.0KB)
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.

2022, 9(3): 283-297 doi: 10.3934/jdg.2022014 +[Abstract](339) +[HTML](250) +[PDF](350.23KB)
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.

2022, 9(3): 299-322 doi: 10.3934/jdg.2022015 +[Abstract](315) +[HTML](97) +[PDF](3087.21KB)
Abstract:

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.

2021 CiteScore: 3.3