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

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.

Pengembangan Game Edukasi dengan Konteks Kearifan Lokal Banten pada Materi Matriks

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.

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

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.

Optimizing Underwater Game Strategy Based on Cooperative Confrontation

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.

A Novel Multiperson Game Approach for Linguistic Multicriteria Decision Making Problems

Game theory is considered as an efficient framework in dealing with decision making problems for two players in the competitive environment. In general, the evaluation values of payoffs matrix are expressed by crisp values in a game model. However, many uncertainties and vagueness should be considered due to the qualitative criteria and the subjective judgment of decision makers in the decision making process. The aim of this study is to develop an effective methodology for solving the payoffs matrix with linguistic variables by multiple decision makers in a game model. Based on the linguistic variables, the decision makers can easily express their opinions with respect to criteria for each alternative. By using the linear programming method, we can find the optimal solution of a game matrix in accordance with the combination of strategies of each player effectively. In addition, the expected performance value (EPV) index is defined in this paper to compare the competition ability of each player based on the optimal probability of each strategy combination. And then, numerical example will be implemented to illustrate the computation process of the proposed model. The conclusion and future research are discussed at the end of this paper.

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

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.

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

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.