• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1497-1510
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• 2019

In this paper we compute the stopping times in the game Rock-Paper-Scissors. By exploiting the recurrence relation we compute the mean values of stopping times. On the other hand, by constructing a transition matrix for a Markov chain associated with the game, we get also the distribution of the stopping times and thereby we compute the mean stopping times again. Then we show that the mean stopping times increase exponentially fast as the number of the participants increases.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.54 no.2
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• pp.97-106
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• 2005

This paper presents a method for evaluating the nash equilibrium of the Cournot model for N-Gencos in wholesale electricity market. In wholesale electricity market, the strategies of N-Gencos can be applied to the game model under the conditions, which the Gencos determine their strategies to maximize their benefit. Generally, the Lemke algorithm has known as the approach to evaluate the mixed nash equilibrium in the only two-player game model. In this paper, we have developed the necessary condition for obtaining the mixed nash equilibrium of N-player by using the Lemke algorithms. However, it is difficult to find the mixed nash equilibrium of two more players by using the analytic method since those have the nonlinear characteristics. To overcome the above problem, we have formulated the object function satisfied with the proposed necessary conditions for N-player nash equilibrium and applied the modified particle swarm optimization (PSO) method to obtain the equilibrium for N-player. To present the effectiveness the proposed necessary condition and the evaluation approach, this paper has shown the results of equilibrium of sample system and the cournot game model for 3-players.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.101-119
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• 2012

The removal of the Go Stones is a game that anyone can play through simple rules. It is not only an interesting game but also a mathematical game that requires comprehensive knowledge of several mathematical theories. Through analyzing the rules and theories of this game, students can get a new mathematical perspective and recognize something that they didn't realize as important before. Furthermore, this game is given to students as a mathematical problem unconsciously. This helps them get a mathematical approach to understanding the actual concept of the problem as well as the basic principle of the problem.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.871-881
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• 2008

In this paper, we study the core stability of the dominating set game which has arisen from the cost allocation problem related to domination problem on graphs. Let G be a graph whose neighborhood matrix is balanced. Applying duality theory of linear programming and graph theory, we prove that the dominating set game corresponding to G has the stable core if and only if every vertex belongs to a maximum 2-packing in G. We also show that for dominating set games corresponding to G, the core is stable if it is large, the game is extendable, or the game is exact. In fact, the core being large, the game being extendable and the game being exact are shown to be equivalent.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2081-2086
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• 2005

This paper proposes the receding horizon $H_{\infty}$ predictive control (RHHPC) for systems with a state-delay. We first proposes a new cost function for a finite horizon dynamic game problem. The proposed cost function includes two terminal weighting terns, each of which is parameterized by a positive definite matrix, called a terminal weighting matrix. Secondly, we derive the RHHPC from the solution to the finite dynamic game problem. Thirdly, we propose an LMI condition under which the saddle point value satisfies the well-known nonincreasing monotonicity. Finally, we shows the asymptotic stability and $H_{\infty}$-norm boundedness of the closed-loop system controlled by the proposed RHHPC. Through a numerical example, we show that the proposed RHHC is stabilizing and satisfies the infinite horizon $H_{\infty}$-norm bound.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.4
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• pp.260-270
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• 2013

This paper proposes a strategic portfolio model for managing performance of online games. The portfolio matrix is composed of two dimensions: financial performance and non-financial performance. Financial performance is measured by the conventional measure, average revenue per user (ARPU). In terms of non-financial performance, five non-financial key performance indicators (KPIs) that have been widely used in the online game industry are utilized: RU (Register User), VU (Visiting User), TS (Time Spent), ACU (Average Current User), MCU (Maximum Current User). Data envelopment analysis (DEA) is then employed to produce a single performance measure aggregating the five KPIs. DEA is a linear programming model for measuring the relative efficiency of decision making unit (DMUs) with multiple inputs and outputs. This study employs DEA as a tool for multiple criteria decision making (MCDM), in particular, the pure output model without inputs. Combining the two types of performance produces the online game portfolio matrix with four quadrants: Dark Horse, Stop Loss, Jack Pot, Luxury Goods. A case study of 39 online games provided by company 'N' is provided. The proposed portfolio model is expected to be fruitfully used for strategic decision making of online game companies.

• International Journal of Internet, Broadcasting and Communication
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• v.13 no.1
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• pp.243-248
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• 2021

Although many different types of covert channels have been suggested in the literature, there are little work in directly applying game theory to building up covert channel. This is because researchers have mainly focused on tailoring game theory for covert channel analysis, identification, and covert channel problem solving. Unlike typical adaptation of game theory to covert channel, we show that game theory can be utilized to establish a new type of covert channel in IoT devices. More specifically, we propose a covert channel that can be constructed by utilizing the Nash Equilibrium with sensor data collected from IoT devices. For covert channel construction, we set random seed to the value of sensor data and make payoff from random number created by running pseudo random number generator with the configured random seed. We generate I × J (I ≥ 2, J ≥ 2) matrix game with these generated payoffs and attempt to obtain the Nash Equilibrium. Covert channel construction method is distinctly determined in accordance with whether or not to acquire the Nash Equilibrium.

• Journal of the Korean Operations Research and Management Science Society
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• v.13 no.1
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• pp.1-9
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• 1988

The purpose of this paper is study the sensitivity analysis of matrix game. Teh sensitivity analysis of matrix is classified into two types. Type one is to find the characteristic region of an element of the pay off matrix in which the value of the current optimal strategy remains as an optimum. Type two is to find that in which the basis of the current optimal strategy does not change. This paper shows the characteristic regions of basic and nonbasic strategies. Further it is found that the characteristic regions of type one and two are same in the case that the element is that of at least one player's nonbasic strategy.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.3
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• pp.509-516
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• 2011

This paper studies a novel method to find the profit-maximizing Nash Equilibriums in allocating generation quantities with consideration of ramp-rates under competitive market environment. Each GenCo in a market participates in a game to maximize its profit through competitions and play a game with bidding strategies. In order to find the Nash equilibriums it is necessary to search the feasible combinations of GenCos' strategies which satisfy every participant's profit and no one wants various constraints. During the procedure to find Nash equilibriums, the payoff matrix can be simplified as eliminating the dominated strategies. in each time interval. Because of the ramp-rate, generator's physically or technically limits to increase or decrease outputs in its range, it can restrict the number of bidding strategies of each generator at the next stage. So in this paper, we found the Nash Equilibriums for multi-stage generation allocation game considering the ramp-rate limits of generators. In the case studies, we analyzed the generation allocation game for a 12-hour multi-stage and compared it with the results of dynamic economic dispatch. Both of the two cases were considered generator's ramp-rate effects.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.53 no.11
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• pp.630-635
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• 2004

Generation companies(Genco) submit the supply functions as a bidding function to a bid market in a competitive electricity market. The profits of Gencos vary in accordance with the bid functions, so the selection of a bidding function plays a key role in increasing their profits. In order to get a profitable bidding function which is usually linear, it is required to modify adequately the intersection and the slope of a linear supply function. This paper presents an analysis of the selection of the supply function from the viewpoint of Nash equilibrium(NE). Four types of bidding function parameters are used for analizing the electricity market. The competition of selecting bidding parameters is modeled as two level games in this research. One is a subgame where a certain type of parameters is given and the players compete to select values of the underlying parameters. The other is an overall game where the players compete to select a profitable type among the four types of parameters. The NEs in both games are computed by an using analytic method and a payoff matrix method. It is verified in case studies for the NE of overall game to satisfy the equilibrium condition.