• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.599-610
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• 2006

The aim of this paper is to give an existence theorem for a strong solution of generalized vector quasi-equilibrium problems of the weak type II due to Hou et al. using the equilibrium existence theorem for 1-person game, and as an application, we shall give a generalized quasivariational inequality.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1297-1310
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• 2008

Main purpose of this paper is to combine the optimal form of Fan's best approximation theorem and Nash's equilibrium existence theorem into a single existence theorem simultaneously. For this, we first prove a general best proximity pair theorem which includes a number of known best proximity theorems. Next, we will introduce a new equilibrium concept for a generalized Nash game with normal form, and as applications, we will prove new existence theorems of Nash equilibrium pairs for generalized Nash games with normal form.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.457-473
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• 2019

In this paper, we investigate weak laws of large numbers for weighted coordinatewise pairwise negative quadrant dependence random vectors in Hilbert spaces in the case that the decay order of tail probability is r for some 0 < r < 2. Moreover, we extend results concerning Pareto-Zipf distributions and St. Petersburg game.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.2
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• pp.109-117
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• 2021

In this paper, as an application of a multivalued generalization of the Németh fixed point theorem, we will prove a new existence theorem of Nash equilibrium for a generalized game 𝓖 = (X_i; A_i, P_i)_i∈I with geodesic convex values in Hadamard manifolds.

• The Journal of the Korea Contents Association
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• v.7 no.9
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• pp.1-9
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• 2007

Recently, the primary school training courses requires creative human being who is able to solve problem in accordance with rapidly changing society. Accordingly, it needs development of edutainment contents that can develop creativity and heighten educational effect as attracting learner's interest. This paper intends to design educational game which can develop creativity. Method of research is based on the concept of creativity and theory of multiple intelligence. First, I pulled out educational elements of edutainment game which can develop ability to solve synthetic problem and then drew interest elements of edutainment game by combined game with form of cartoon. Secondly, creativity studying area set the 5 learning area of verbal, visual, mathematical, logical and analytic creativity and then, a course of learning was designed to have each 3 details of 5 teaming areas of creativity. Finally, it presented production direction of educational game by combined with 4 elements of the interest that is an avatar, achievement of a mission, a time limit and win a point.

• Journal of Korea Game Society
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• v.13 no.2
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• pp.49-58
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• 2013

In this study, a tree growth model is designed to represent a variety of trees consisting of a outdoor terrain of game efficiently and naturally. The proposed tree growth model is an integrated tree growth model, and is configured using the following approaches: (1) the tree modeling method based on growth volume and the convolution sums of divisor functions, which is used to model a variety kind of trees more intuitively and naturally; (2) a rendering method using a level of detail of branch based on instancing for real-time processing of numerous trees with complicated structures; and (3) a combination of the above methods to efficiently implement a game landscape. The natural and diverse growths of trees that emerged using the proposed tree growth model is evaluated through experimentation, along with the possibility of implementing the natural game landscape and the efficiency of real-time processing.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.253-261
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• 2004

Game theory is mathematical analysis developed to study involved in making decisions. In 1928, Von Neumann proved that every two-person, zero-sum game with finitely many pure strategies for each player is deterministic. As well, in the early 50's, Nash presented another concept as the basis for a generalization of Von Neumann's theorem. Another central achievement of game theory is the introduction of evolutionary game theory, by which agents can play optimal strategies in the absence of rationality. Not the rationality but through the process of Darwinian selection, a population of agents can evolve to an Evolutionary Stable Strategy (ESS) introduced by Maynard Smith. Keeping pace with these game theoretical studies, the first computer simulation of co-evolution was tried out by Hillis in 1991. Moreover, Kauffman proposed NK model to analyze co-evolutionary dynamics between different species. He showed how co-evolutionary phenomenon reaches static states and that these states are Nash equilibrium or ESS introduced in game theory. Since the studies about co-evolutionary phenomenon were started, however many other researchers have developed co-evolutionary algorithms, in this paper we propose Game theory based Co-Evolutionary Algorithm (GCEA) and confirm that this algorithm can be a solution of evolutionary problems by searching the ESS.To evaluate newly designed GCEA approach, we solve several test Multi-objective Optimization Problems (MOPs). From the results of these evaluations, we confirm that evolutionary game can be embodied by co-evolutionary algorithm and analyze optimization performance of GCEA by comparing experimental results using GCEA with the results using other evolutionary optimization algorithms.

• Industrial Engineering and Management Systems
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• v.12 no.3
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• pp.264-273
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• 2013

Credit option is a policy that has been studied by many researchers in the area of supply chain management. This policy has been applied in practice to improve the profits of supply chain members. Usually, a credit option policy is proposed by the seller, and often under a symmetric information environment where members have complete information on each others' operations. In this paper, we investigate two scenarios: firstly, the seller offers a credit option to the buyer, and secondly, the buyer attempts to stretch the length of the credit period offered by the seller. The proposed model in both scenarios will be investigated under an asymmetric information structure where some information are private and are only known to the individual who has knowledge of this information. The interactions between buyer and seller will be modeled by non-cooperative Stackelberg games where the buyer and seller take turn as leader and follower. Among some of the numerical results obtained, the seller and buyer's profits obtained from symmetric information games are larger than those obtained from an asymmetric information game in both scenarios. Furthermore, both buyer and seller's profit in the second scenario are better than in the first scenario.

• Industrial Engineering and Management Systems
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• v.12 no.3
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• pp.207-223
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• 2013

Revenue management (RM) has been widely used to model products characterized as perishable. Classical RM model assumed that price is the sole factor in the model. Thus price adjustment becomes a crucial and costly factor in business. In this paper, an optimal pricing model is developed based on minimization of soft customer cost, one kind of price adjustment cost and is solved by Lagrange multiplier method. It is formed by expected discounted revenue/bid price integrating quantity-based RM and pricing-based RM. Quantity-based RM consists of two capacity models, namely, booking limit and overbooking. Booking limit, built by assuming uncertain customer arrival, decides the optimal capacity allocation for two market segments. Overbooking determines the level of accepted order exceeding capacity to anticipate probability of cancellation. Furthermore, pricing-based RM models occupancy/demand rate influenced by internal and competitor price changes. In this paper, a mathematical model based on game theoretic approach is developed for two conditions of deterministic and stochastic demand. Based on the equilibrium point, the best strategy for both hotels can be determined.

• Communications of Mathematical Education
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• v.33 no.2
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• pp.67-84
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• 2019

The purpose of this study is to investigate the effectiveness of intensive inquiry activity through intensive camp for 2 hours and 3 days in summer vacation and 100 hours of classes from March to December 2018 by selecting 2 middle school students using OKMINDMAP for creative education. It is the result. The teacher was the assistant, and the research problem was selected by two students themselves, and the variation of the fractal dimension was investigated and the Chaos game was shown to be possible in the modified Sierpinski triangle.