An Eigenvalue Formula for the Radius of Stability of a Stable Game Matrix

1990 ◽  
Vol 11 (3) ◽  
pp. 369-372
Author(s):  
Marvin D. Troutt
Keyword(s):  
Game Matrix

Analysis of the Possibilities of Using the Wald-Savage Test for the Study of Game Models

2021 ◽  
Vol 9 (4) ◽  
pp. 82-88
Author(s):  
Dmitriy Vlasov
Keyword(s):  
Optimality Criterion ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Optimality Criteria ◽  
Advanced Training ◽  
Investment Strategies ◽  
Optimal Investment Strategy ◽  
Game Matrix ◽  
States Of Nature ◽  
Savage Criterion

Within the framework of this article, the mechanisms for constructing and researching the game model for choosing the investor's optimal investment strategy in various information conditions are disclosed: building many players, building many players' strategies, the option of formalizing the payment function in the form of a game matrix, many optimality criteria, methods of justifying the choice of the strategy optimality criterion. Against the background of the application of classical criteria (Savage criterion, Wald criterion, Hodge-Lehman criterion, Hermeyer criterion), special attention is paid to the analysis of the possibilities of using the integrated Wald-Savage criterion for the study of game models, which allows to smooth the shortcomings of classical criteria and take into account the investor's appetite for risk. Attention is focused on the need to justify the choice of the criterion for the optimality of investment strategies, as well as the need of the researcher to clarify the states of nature and the probabilities of their implementations. The mechanisms for constructing and researching game models presented in this article can be used to improve methodological systems for teaching applied mathematical disciplines at an economic university, to build new variable educational disciplines on modern issues of decision theory, as well as within the framework of the system of advanced training in economics.

A WEAKENED FORM OF FICTITIOUS PLAY IN TWO-PERSON ZERO-SUM GAMES

2000 ◽  
Vol 02 (04) ◽  
pp. 307-328 ◽  
Author(s):  
BEN VAN DER GENUGTEN
Keyword(s):  
Optimal Strategies ◽  
Fictitious Play ◽  
Large Games ◽  
Zero Sum Games ◽  
Game Matrix ◽  
Numerical Iteration ◽  
Speed Up ◽  
New Form ◽  
Zero Sum ◽  
Weakened Form

Fictitious play can be seen as a numerical iteration procedure for determining the value of a game and corresponding optimal strategies. Although convergence is slow, it needs only a modest computer storage. Therefore it seems to be a good way for analysing large games. In this paper we introduce a weakened form of fictitious play, where players at each stage do not have to make the best choice against the total of past choices of the other player but only an increasingly better one. Theoretical bounds for convergence are derived. Furthermore, it is shown that this new form can speed up convergence considerably in practice. It is seen that weakened fictitious play can be extended to models in which the game matrix itself becomes better known as the number of stages increases.

scholarly journals Optimizing Underwater Game Strategy Based on Cooperative Confrontation

2019 ◽  
Vol 37 (1) ◽  
pp. 63-69 ◽  
Author(s):  
Na Wei ◽  
Mingyong Liu ◽  
Shuai Zhang ◽  
Xiaojian Zhang
Keyword(s):  
Nash Equilibrium ◽  
Autonomous Underwater Vehicles ◽  
Dynamic Game ◽  
Allocation Model ◽  
Nash Equilibrium Point ◽  
Defense Strategies ◽  
Underwater Environment ◽  
Game Matrix ◽  
Attack And Defense ◽  
Probability Index

Based on the multi-round confrontation of multiple Autonomous Underwater Vehicles (AUVS), the concept of Nash equilibrium is used to solve the problem of underwater dynamic cooperative confrontation of multiple AUVs. From the perspective of confrontation strategies of both sides of an AUV and considering the influence of survival probability index function and the uncertain factors of underwater environment, the unit target allocation model of multiple AUVs based on dynamic game and game matrix are established. By solving the Nash equilibrium solution of the game model, the particle swarm optimization algorithm is applied to solve the Nash equilibrium point for obtaining the optimal attack and defense strategies of both sides. The feasibility and effectiveness of the method was verified by simulation.

scholarly journals A Competitive Multiattribute Group Decision-Making Approach for the Game between Manufacturers

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Quan Zhang ◽  
KeXin Jiang ◽  
ManTing Yan ◽  
JiYun Ma
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Evidence Theory ◽  
Practical Case ◽  
Game Matrix ◽  
Decision Making Problem ◽  
Dimension 2 ◽  
Evaluation Information

Under the competitive market environment, the game between manufacturers comes down to the competitive multiattribute group decision-making problem. In this study, the evaluation information of experts is given in the form of 2-dimension 2-tuple linguistic variables, and an approach is proposed for the competitive multiattribute group decision-making problem based on game theory and evidence theory. Firstly, based on the evidence theory, the attribute values of each situation are obtained by aggregating the 2-dimension 2-tuple linguistic evaluation information given by experts. Secondly, according to the attribute values of every situation, the evidence theory is applied for the second aggregation to obtain the overall values of every situation, and then the game matrix of competitive multiattribute group decision problem is formed. Then, according to the bivariate game matrix, the Nash equilibrium point of competitive multiattribute group decision-making problem is determined based on game theory. Finally, a practical case about the alternative selections for a duopoly problem is used to illustrate the effectiveness and applicability of the proposed approach for the competitive multiattribute group decision-making problem.

Game Analysis of People-Post Matching among the Middle Managers in Enterprises

2012 ◽  
Vol 452-453 ◽  
pp. 1079-1083
Author(s):  
Te Ming Liao ◽  
Xiao Mei Du
Keyword(s):  
Business Performance ◽  
Middle Managers ◽  
Strategic Objectives ◽  
Game Analysis ◽  
Portfolio Strategy ◽  
The People ◽  
Game Matrix ◽  
Management And Development ◽  
Strategy Game

The middle managers shoulder the important responsibility in the enterprise. The middle managers stress executive capability. But the executive result affects business performance directly. In order to realize strategic objectives, the enterprises must strengthen management and development of the middle managers on the base of people-post matching.The paper analyses the game between the enterprise and the middle managers on the base of the meaning and status of people-post matching. The paper builds the game matrix and portfolio strategy game. The game analysis provides decision basis for the people-post matching and development of the middle managers.

scholarly journals Pengembangan Game Edukasi dengan Konteks Kearifan Lokal Banten pada Materi Matriks

2020 ◽  
Vol 4 (2) ◽  
pp. 319
Author(s):  
Arum Widya Safitri ◽  
Heni Pujiastuti ◽  
Ria Sudiana
Keyword(s):  
Mathematics Teachers ◽  
Field Research ◽  
Learning Activities ◽  
Development Model ◽  
Educational Game ◽  
Questionnaire Validation ◽  
Game Matrix ◽  
Learning Mathematics ◽  
Teachers And Students ◽  
Analysis Design

ABSTRAK Tujuan penelitian adalah menghasilkan produk game edukasi matematika sebagai media pembelajaran matematika dengan konteks kearifan lokal Banten yang layak, efektif serta praktis dan dapat digunakan dilapangan. Penelitian pengembangan ini dilakukan dengan mengadopsi model pengembangan ADDIE yang terdiri dari lima tahap yaitu analyze (analisis), design (perancangan), development (pengembangan), implementation (implementasi), serta evaluation (evaluasi). Instrumen yang digunakan yaitu lembar angket validasi ahli, lembar angket respons guru matematika dan siswa, serta lembar ketuntasan level game. Adapun hasil yang diperoleh yaitu bahwa game edukasi layak, praktis, dan efektif digunakan pada kegiatan pembelajaran. Kata kunci: game edukasi, matriks, kearifan lokal.   ABSTRACT The research objective is to produce educational math games as a medium of learning mathematics with the context of local wisdom Bantam a viable, effective and practical and can be used in the field. Research and development is done by adopting the development model of ADDIE which consists of five stages: analyze (analysis), design (perancangan), development (pengembangan), implementation (implementation), and evaluation (evaluation). The instrument used in the sheet questionnaire validation experts, sheet questionnaire responses of mathematics teachers and students, as well as the sheet mastery level the game. The results obtained, namely that the game is feasible, practical, and effective to use in learning activities. Keywords: educational game, matrix, local wisdom.

scholarly journals Transformation of game matrix and game value

1964 ◽  
Vol 4 (1) ◽  
pp. 25-29
Author(s):  
E. Vilkas
Keyword(s):  
Game Matrix ◽  
Game Value

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Э. И. Вилкас. Преобразования матрицы игры и значения игры E. Vilkas. Lošimo matricos ir lošimo reikšmės transformacijos

scholarly journals METHOD TO SOLVE FUZZY GAME MATRIX

2014 ◽  
Vol 89 (5) ◽  
Author(s):  
S. Kumar ◽  
R. Chopra ◽  
R.R. Saxena
Keyword(s):  
Game Matrix ◽  
Fuzzy Game
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