scholarly journals On some general scheme of constructing iterative methods for searching the Nash equilibrium in concave games

2021 ◽  
Vol 13 (3) ◽  
pp. 75-121
Author(s):  
Андрей Владимирович Чернов ◽  
Andrey Chernov
Keyword(s):  
Nash Equilibrium ◽  
Iterative Process ◽  
Numerical Experiments ◽  
General Scheme ◽  
Iterative Algorithms ◽  
Specific Character ◽  
Residual Function ◽  
Arbitrary Continuous Function ◽  
Finite Dimensional ◽  
The Subject

The subject of the paper is finite-dimensional concave games id est noncooperative $n$-person games with objective functionals concave with respect to `their own' variables. For such games we investigate the problem of designing iterative algorithms for searching the Nash equilibrium with convergence guaranteed without requirements concerning objective functionals such as smoothness and as convexity in `strange' variables or another similar hypotheses (in the sense of weak convexity, quasiconvexity and so on). In fact, we prove some assertion analogous to the theorem on convergence of $M$-Fej\'{er iterative process for the case when an operator acts in a finite-dimensional compact and nearness to an objective set is measured with the help of arbitrary continuous function. Then, on the base of this assertion we generalize and develop the approach suggested by the author formerly to searching the Nash equilibrium in concave games. The last one can be regarded as "a cross between" the relaxation algorithm and the Hooke-Jeeves method of configurations (but taking into account a specific character of the the residual function being minimized). Moreover, we present results of numerical experiments with their discussion.

An experimental study of a DC optimization algorithm for bimatrix games

2020 ◽  
pp. 2150143
Author(s):  
Aicha Anzi ◽  
Ramzi Kasri ◽  
Hicham Lenouar ◽  
Mohammed Said Radjef
Keyword(s):  
Experimental Study ◽  
Nash Equilibrium ◽  
Linear Complementarity Problem ◽  
Optimization Algorithm ◽  
Numerical Experiments ◽  
General Scheme ◽  
Linear Complementarity ◽  
Bimatrix Games ◽  
Difference Of Convex ◽  
The Difference

This paper presents a nonconvex approach for computing a Nash equilibrium in bimatrix games. It relies on the Linear Complementarity Problem (LCP) formulation of the game and follows the Difference of Convex Algorithm (DCA) general scheme. To measure the performance of the proposed approach, numerical experiments as well as a comparative study with the Lemke Howson (LH) algorithm are carried out.

scholarly journals Impact of Demerger on Shareholders’ Wealth

2009 ◽  
Vol 1 (1) ◽  
Author(s):  
Ranjit SINGH ◽  
Amalesh BHOWAL ◽  
Varun BAWARI
Keyword(s):  
Value Creation ◽  
Stock Exchange ◽  
Specific Character ◽  
Average Price ◽  
Share Prices ◽  
The Subject ◽  
Time Specific ◽  
Almost All ◽  
Total Wealth

Purpose – The purpose of this paper is to investigate the change in the level of the wealth of the shareholders’ before the demerger and after the demerger.Design/methodology/approach – In the present study the data relating to share prices has been taken from the official website of Bombay Stock Exchange. Here the average of the six months price of the demerged company before demerger and average six months price or the average price upto 31st of July, 2007 has been collected of demerged and resultant company after demerger. Findings – It is found that after demerger there is increase in the total wealth of the shareholders in almost all the cases.Research limitations/implications – Given the nature of this study, generalizations cannot be made as the study is conducted in a bullish market. The time specific character of the subject matter is an opportunity for future longitudinal research.Practical implications – Presently de-mergers are creating enormous wealth for shareholders. It is because of the negative synergy. Due to the demerger this negative synergy is removed and the value is unlocked. However, Investors should differentiate between genuine attempts at value creation and de-mergers undertaken to create hype around the stocks. Stay away from dubious companies that want to manipulate prices. Investors should focus on the quality of management and corporate governance record of the companyOriginality/value – The study is the first of its kind and hence original in nature.Article Type: Research paperKeyword(s): Demerger, Demerged Company, Resultant Company, Negative Synergy, Shareholders Wealth.

scholarly journals Singular Points of Curves

2018 ◽  
Vol 25 (6) ◽  
pp. 692-710
Author(s):  
Artem D. Uvarov
Keyword(s):  
Iterative Process ◽  
Geometric Modeling ◽  
Global Minimum ◽  
Iterative Algorithms ◽  
Singular Points ◽  
Intersection Curve ◽  
Software Environment ◽  
Advantages And Disadvantages ◽  
Intersection Curves ◽  
Complex Cases

In this paper, we consider the key problem of geometric modeling, connected with the construction of the intersection curves of surfaces. Methods for constructing the intersection curves in complex cases are found: by touching and passing through singular points of surfaces. In the first part of the paper, the problem of determining the tangent line of two surfaces given in parametric form is considered. Several approaches to the solution of the problem are analyzed. The advantages and disadvantages of these approaches are revealed. The iterative algorithms for finding a point on the line of tangency are described. The second part of the paper is devoted to methods for overcoming the difficulties encountered in solving a problem for singular points of intersection curves, in which a regular iterative process is violated. Depending on the type of problem, the author dwells on two methods. The first of them suggests finding singular points of curves without using iterative methods, which reduces the running time of the algorithm of plotting the intersection curve. The second method, considered in the final part of the article, is a numerical method. In this part, the author introduces a function that achieves a global minimum only at singular points of the intersection curves and solves the problem of minimizing this function. The application of this method is very effective in some particular cases, which impose restrictions on the surfaces and their arrangement. In conclusion, this method is considered in the case when the function has such a relief, that in the neighborhood of the minimum point the level surfaces are strongly elongated ellipsoids. All the images given in this article are the result of the work of algorithms on methods proposed by the author. Images are built in the author’s software environment.

scholarly journals Operant Matching as a Nash Equilibrium of an Intertemporal Game

2009 ◽  
Vol 21 (10) ◽  
pp. 2755-2773 ◽  
Author(s):  
Yonatan Loewenstein ◽  
Drazen Prelec ◽  
H. Sebastian Seung
Keyword(s):  
Nash Equilibrium ◽  
Matching Law ◽  
Single Subject ◽  
Multiple Selves ◽  
The Past ◽  
Aggregate Behavior ◽  
The Subject ◽  
Individual Choices ◽  
The Relationship ◽  
Mutual Defection

Over the past several decades, economists, psychologists, and neuroscientists have conducted experiments in which a subject, human or animal, repeatedly chooses between alternative actions and is rewarded based on choice history. While individual choices are unpredictable, aggregate behavior typically follows Herrnstein's matching law: the average reward per choice is equal for all chosen alternatives. In general, matching behavior does not maximize the overall reward delivered to the subject, and therefore matching appears inconsistent with the principle of utility maximization. Here we show that matching can be made consistent with maximization by regarding the choices of a single subject as being made by a sequence of multiple selves—one for each instant of time. If each self is blind to the state of the world and discounts future rewards completely, then the resulting game has at least one Nash equilibrium that satisfies both Herrnstein's matching law and the unpredictability of individual choices. This equilibrium is, in general, Pareto suboptimal, and can be understood as a mutual defection of the multiple selves in an intertemporal prisoner's dilemma. The mathematical assumptions about the multiple selves should not be interpreted literally as psychological assumptions. Human and animals do remember past choices and care about future rewards. However, they may be unable to comprehend or take into account the relationship between past and future. This can be made more explicit when a mechanism that converges on the equilibrium, such as reinforcement learning, is considered. Using specific examples, we show that there exist behaviors that satisfy the matching law but are not Nash equilibria. We expect that these behaviors will not be observed experimentally in animals and humans. If this is the case, the Nash equilibrium formulation can be regarded as a refinement of Herrnstein's matching law.

Chapter 8 Constant Capital and Variable Capital

Capital ◽  
2008 ◽  
Author(s):  
Karl Marx
Keyword(s):  
Specific Character ◽  
Labour Process ◽  
The Subject ◽  
Different Parts

The various factors of the labour-process play different parts in forming the value of the product. The labourer adds fresh value to the subject of his labour by expending upon it a given amount of additional labour, no matter what the specific character and utility...

scholarly journals Insights of professional activity at the stage of professionalization

2019 ◽  
Vol 70 ◽  
pp. 07008
Author(s):  
Svetlana Zholudeva ◽  
Irina Ulybysheva
Keyword(s):  
Empirical Study ◽  
Self Determination ◽  
Professional Activity ◽  
High Tech ◽  
Specific Character ◽  
Highly Qualified ◽  
Dynamic Development ◽  
Qualified Personnel ◽  
Self Actualization ◽  
The Subject

Specific character of a dynamic development of economy and society place demands on new highly-qualified personnel of any sphere professional activity, especially the sphere connected with interaction with people who have modern high-tech skills. Demands’ changes on the subject of professional activity brings on a qualitative restructuring of professionalization’s process, that facilitates an integration of educational and professional spheres with a conceptional, technological and theoretical supporting. Successful professional activity depends a lot upon a successful period of early professionalization that is impossible without proper provided insights of a profession. This article shows the results of an empirical study regarding the analysis of peculiarities of professional ideas of pre-service teachers. A specific attention is given to the problem of study of professional activity ideas effect at the stage of early professionalization, which changes during the period of ideas’ transformation concerning professional activity and career building that is caused by the changes in the essence of professionalization from a socio normed event into an individual work of professional aimed at self-determination and self-actualization in profession.

scholarly journals Complete slices and homological properties of tilted algebras

1994 ◽  
Vol 36 (3) ◽  
pp. 347-354 ◽  
Author(s):  
Ibrahim Assem ◽  
Flávio Ulhoa Coelho
Keyword(s):  
Representation Theory ◽  
Global Dimension ◽  
Indecomposable Modules ◽  
Tilted Algebra ◽  
Finite Dimensional ◽  
Tilted Algebras ◽  
Homological Dimensions ◽  
The Subject ◽  
Left And Right ◽  
Almost All

It is reasonable to expect that the representation theory of an algebra (finite dimensional over a field, basic and connected) can be used to study its homological properties. In particular, much is known about the structure of the Auslander-Reiten quiver of an algebra, which records most of the information we have on its module category. We ask whether one can predict the homological dimensions of a module from its position in the Auslander-Reiten quiver. We are particularly interested in the case where the algebra is a tilted algebra. This class of algebras of global dimension two, introduced by Happel and Ringel in [7], has since then been the subject of many investigations, and its representation theory is well understood by now (see, for instance, [1], [7], [8], [9], [11], [13]).In this case, the most striking feature of the Auslander-Reiten quiver is the existence of complete slices, which reproduce the quiver of the hereditary algebra from which the tilted algebra arises. It follows from well-known results that any indecomposable successor (or predecessor) of a complete slice has injective (or projective, respectively) dimension at most one, from which one deduces that a tilted algebra is representation-finite if and only if both the projective and the injective dimensions of almost all (that is, all but at most finitely many non-isomorphic) indecomposable modules equal two (see (3.1) and (3.2)). On the other hand, the authors have shown in [2, (3.4)] that a representation-infinite algebra is concealed if and only if both the projective and the injective dimensions of almost all indecomposable modules equal one (see also [14]). This leads us to consider, for tilted algebras which are not concealed, the case when the projective (or injective) dimension of almost all indecomposable successors (or predecessors, respectively) of a complete slice equal two. In order to answer this question, we define the notions of left and right type of a tilted algebra, then those of reduced left and right types (see (2.2) and (3.4) for the definitions).

An Iterative algorithm for $\eta$-(anti)-Hermitian least-squares solutions of quaternion matrix equations

2015 ◽  
Vol 30 ◽  
Author(s):  
Fatemeh Beik ◽  
Salman Ahmadi-Asl
Keyword(s):  
Least Squares ◽  
Iterative Algorithm ◽  
Numerical Experiments ◽  
Iterative Algorithms ◽  
Iterative Approach ◽  
Matrix Equations ◽  
Quaternion Matrix ◽  
Hermitian Matrices ◽  
Convergence Properties ◽  
Least Squares Problems

Recently, some research has been devoted to finding the explicit forms of the η-Hermitian and η-anti-Hermitian solutions of several kinds of quaternion matrix equations and their associated least-squares problems in the literature. Although exploiting iterative algorithms is superior than utilizing the explicit forms in application, hitherto, an iterative approach has not been offered for finding η-(anti)-Hermitian solutions of quaternion matrix equations. The current paper deals with applying an efficient iterative manner for determining η-Hermitian and η-anti-Hermitian least-squares solutions corresponding to the quaternion matrix equation AXB + CY D = E. More precisely, first, this paper establishes some properties of the η-Hermitian and η-anti-Hermitian matrices. These properties allow for the demonstration of how the well-known conjugate gradient least- squares (CGLS) method can be developed for solving the mentioned problem over the η-Hermitian and η-anti-Hermitian matrices. In addition, the convergence properties of the proposed algorithm are discussed with details. In the circumstance that the coefficient matrices are ill-conditioned, it is suggested to use a preconditioner for accelerating the convergence behavior of the algorithm. Numerical experiments are reported to reveal the validity of the elaborated results and feasibility of the proposed iterative algorithm and its preconditioned version.

scholarly journals Contact lines over random topographical substrates. Part 1. Statics

2011 ◽  
Vol 672 ◽  
pp. 358-383 ◽  
Author(s):  
NIKOS SAVVA ◽  
GRIGORIOS A. PAVLIOTIS ◽  
SERAFIM KALLIADASIS
Keyword(s):  
Numerical Experiments ◽  
Random Variable ◽  
Contact Angles ◽  
Contact Lines ◽  
Substrate Roughness ◽  
Random Functions ◽  
Flat Substrate ◽  
The Subject ◽  
Influence Of Substrate ◽  
Theoretical Results

We investigate theoretically the statistics of the equilibria of two-dimensional droplets over random topographical substrates. The substrates are appropriately represented as families of certain stationary random functions parametrized by a characteristic amplitude and wavenumber. In the limit of shallow topographies and small contact angles, a linearization about the flat-substrate equilibrium reveals that the droplet footprint is adequately approximated by a zero-mean, normally distributed random variable. The theoretical analysis of the statistics of droplet shift along the substrate is highly non-trivial. However, for weakly asymmetric substrates it can be shown analytically that the droplet shift approaches a Cauchy random variable; for fully asymmetric substrates its probability density is obtained via Padé approximants. Generalization to arbitrary stationary random functions does not change qualitatively the behaviour of the statistics with respect to the characteristic amplitude and wavenumber of the substrate. Our theoretical results are verified by numerical experiments, which also suggest that on average a random substrate neither enhances nor reduces droplet wetting. To address the question of the influence of substrate roughness on wetting, a stability analysis of the equilibria must be performed so that we can distinguish between stable and unstable equilibria, which in turn requires modelling the dynamics. This is the subject of Part 2 of this study.

scholarly journals NUMERICAL EXPERIMENTS FOR THE ESTIMATION OF MEAN DENSITIES OF RANDOM SETS

2014 ◽  
Vol 33 (2) ◽  
pp. 83 ◽  
Author(s):  
Federico Camerlenghi ◽  
Vincenzo Capasso ◽  
Elena Villa
Keyword(s):  
Numerical Experiments ◽  
Random Sets ◽  
Density Estimator ◽  
Absolutely Continuous ◽  
Minkowski Content ◽  
Closed Sets ◽  
Random Closed Sets ◽  
Spatially Inhomogeneous ◽  
The Subject ◽  
Theoretical Results

Many real phenomena may be modelled as random closed sets in ℝd, of different Hausdorff dimensions. The problem of the estimation of pointwise mean densities of absolutely continuous, and spatially inhomogeneous, random sets with Hausdorff dimension n < d, has been the subject of extended mathematical analysis by the authors. In particular, two different kinds of estimators have been recently proposed, the first one is based on the notion of Minkowski content, the second one is a kernel-type estimator generalizing the well-known kernel density estimator for random variables. The specific aim of the present paper is to validate the theoretical results on statistical properties of those estimators by numerical experiments. We provide a set of simulations which illustrates their valuable properties via typical examples of lower dimensional random sets.

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