Wyniki wyszukiwania - BazTech

1

Using Polymatrix Extensive Stackelberg Games in Security – Aware Resource Allocation and Task Scheduling in Computational Clouds

Jakóbik A., Wilczyński A.

Journal of Telecommunications and Information Technology

|

2017

|

nr 1

71--80

EN

In this paper, the Stackelberg game models are used for supporting the decisions on task scheduling and resource utilization in computational clouds. Stackelberg games are asymmetric games, where a specific group of players’ acts first as leaders, and the rest of the players follow the leaders’ decisions and make their decisions based on the leader’s actions. In the proposed model, the optimal schedules are generated under the security criteria along with the generation of the optimal virtual machines set for the scheduled batch of tasks. The security criteria are defined as security requirements for mapping tasks onto virtual machines with specified trust level. The effectiveness of the proposed method has been verified in the realistic use cases with in the cloud environment with OpenStack and Amazon Cloud standards.

2

Stackelberg Security Games: Models, Applications and Computational Aspects

Wilczyński A., Jakóbik A., Kołodziej J.

Journal of Telecommunications and Information Technology

|

2016

|

nr 3

70--79

EN

Stackelberg games are non-symmetric games where one player or specified group of players have the privilege position and make decision before the other players. Such games are used in telecommunication and computational systems for supporting administrative decisions. Recently Stackleberg games became useful also in the systems where security issues are the crucial decision criteria. In this paper authors briefly survey the most popular Stackelberg security game models and provide the analysis of the model properties illustrated in the realistic use cases.

3

Computing the Stackelberg/Nash equilibria using the extraproximal method: Convergence analysis and implementation details for Markov chains games

Trejo K. K., Clempner J. B., Poznyak A. S.

International Journal of Applied Mathematics and Computer Science

|

2015

|

Vol. 25, no. 2

337--351

EN

In this paper we present the extraproximal method for computing the Stackelberg/Nash equilibria in a class of ergodic controlled finite Markov chains games. We exemplify the original game formulation in terms of coupled nonlinear programming problems implementing the Lagrange principle. In addition, Tikhonov's regularization method is employed to ensure the convergence of the cost-functions to a Stackelberg/Nash equilibrium point. Then, we transform the problem into a system of equations in the proximal format. We present a two-step iterated procedure for solving the extraproximal method: (a) the first step (the extra-proximal step) consists of a “prediction” which calculates the preliminary position approximation to the equilibrium point, and (b) the second step is designed to find a “basic adjustment” of the previous prediction. The procedure is called the “extraproximal method” because of the use of an extrapolation. Each equation in this system is an optimization problem for which the necessary and efficient condition for a minimum is solved using a quadratic programming method. This solution approach provides a drastically quicker rate of convergence to the equilibrium point. We present the analysis of the convergence as well the rate of convergence of the method, which is one of the main results of this paper. Additionally, the extraproximal method is developed in terms of Markov chains for Stackelberg games. Our goal is to analyze completely a three-player Stackelberg game consisting of a leader and two followers. We provide all the details needed to implement the extraproximal method in an efficient and numerically stable way. For instance, a numerical technique is presented for computing the first step parameter (λ) of the extraproximal method. The usefulness of the approach is successfully demonstrated by a numerical example related to a pricing oligopoly model for airlines companies.

4

Ustalona a preferowana kolejność ruchów w grze pojedynczej

Laskowski S.

Telekomunikacja i Techniki Informacyjne

|

2007

|

nr 3-4

10-29

PL

Przeanalizowano dwuosobowe gry o sumie niezerowej pod kątem preferowanej dla graczy kolejności ruchów, ich związku z faktem istnienia lub nieistnienia równowagi Nasha, związku z modelami gry Stackelberga oraz konieczności wykonywania ruchów w określonej kolejności.

EN

An analyses of two-person non-zero sum games in the context of preferable order of the players moves, and their relationship with the fact of existing or non existing Nash equilibrium, with the models of Stackelberg games and with the necessity of making a move in a given order was made.