• 한국시뮬레이션학회논문지
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• 제27권1호
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• pp.39-49
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• 2018

잠수함으로부터 발사되는 SLBM은 은밀성으로 인해 탐지가 매우 제한적이며 이는 안보에 심각한 위협으로 인식된다. 본 연구는 SLBM의 효과적인 탐지를 위한 구축함 배치 최적화 문제를 고려한다. 최적화 모델은 2인 제로섬 게임을 기반으로 하여, 상대방의 입장에서 SLBM이 최대한 탐지되지 않는 발사 및 도착 지점과 비행궤적을 결정하고자 하며, 우리의 입장에서는 상대방의 SLBM 탐지를 최대화할 수 있는 구축함의 배치 계획을 수립한다. 제시된 2인 제로섬 게임 모델은 선형계획법으로 변환하여 최적해를 구할 수 있으며, 가상의 임의 구역과 시나리오를 생성하여 계산 실험을 수행하고 본 연구에서 제시하는 모델을 통해 게임에서의 상대방과 우리의 최적 혼합전략을 도출한 결과를 보여준다.

• 한국경영과학회지
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• 제6권1호
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• pp.71-74
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• 1981

The purpose is to discuss the relationship between zero-sum two-person game with vector-payoff and multiple objective linear program. Further this paper shows that game against nature with vector payoff can be reduced to linear program.

• 한국경영과학회지
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• 제6권2호
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• pp.21-23
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• 1981

It is known that two-person zero-sum game with vector payoff can be reduced to a multiple objective linear programming. However, in this case, solutions for the game nay not be one, but many, In many cases in reality, one may need only one solution rather than all solutions. This paper develops a method to find a practical solution for the game by linear programming.

• 한국국방경영분석학회지
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• 제31권1호
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• pp.107-121
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• 2005

In this study, a new fictitious play (FP) procedure is presented to solve two-person zero-sum (TPZS) Blotto games. The FP solution procedure solves TPZS games by assuming that the two players take turns selecting optimal responses to the opponent's strategy observed so far. It is known that FP converges to an optimal solution, and it may be the only realistic approach to solve large games. The algorithm uses dynamic programming (DP) to solve FP subproblems. Efficiency is obtained by limiting the growth of the DP state space. Blotto games are frequently used to solve simple missile defense problems. While it may be unlikely that the models presented in this paper can be used directly to solve realistic offense and defense problems, it is hoped that they will provide insight into the basic structure of optimal and near-optimal solutions to these important, large games, and provide a foundation for solution of more realistic, and more complex, problem

• 한국경영과학회지
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• 제7권2호
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• pp.53-58
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• 1982

‘섰다’ 게임은 흔히 애용되는 게임이다. 이 논문은 이 섰다 게임의 모형화를 시도한 것으로써 특히 2人섰다게임을 2인영합게임 (two-person zero-sum game)으로 모형화하여 최적해를 구해 보았다. 이 2人섰다 게임은 선과 또 한 사람사이의 섰다게임으로 판돈과 설 때 내는 돈의 액수에 따라 최적해가 달라지는 데 예로써 판돈보다 설 때 내는 돈이 3배일 때는 선은 7끗 이상일 때서는 것이 최적이고 상대방은 9끗 이상일 때서는 것이 최적이다. 이때 게임의 값은 -0.35이다.

• 경영과학
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• 제26권1호
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• pp.1-5
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• 2009

I study a solution concept which preserves the nice Nash equilibrium properties of two-person zero-sum games, and define a locally competitive equilibrium which is characterized by a saddle point with respect to the coordinates of strategies. I show that a locally competitive equilibrium shares the properties of uniqueness of equilibrium payoffs, interchangeablity of equilibrium strategies and convexity of the equilibrium set.

• 한국게임학회 논문지
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• 제1권1호
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• pp.61-67
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• 2001

This paper describes a program which learns good strategies for two-poison, deterministic, zero-sum board games of perfect information. The program learns by simply playing the game against either a human or computer opponent. The results of the program's teaming of a lot of games are reported. The program consists of search kernel and a move generator module. Only the move generator is modified to reflect the rules of the game to be played. The kernel uses a temporal difference procedure combined with a backpropagation neural network to team good evaluation functions for the game being played. Central to the performance of the program is the search procedure. This is a the capture tree search used in most successful janggi playing programs. It is based on the idea of using search to correct errors in evaluations of positions. This procedure is described, analyzed, tested, and implemented in the game-teaming program. Both the test results and the performance of the program confirm the results of the analysis which indicate that search improves game playing performance for sufficiently accurate evaluation functions.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.15-15
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• 2003

We provide some recent results of approximation algorithms for solving Markov Games and discuss their applications to problems that arise in Computer Science. We consider a receding horizon approach as an approximate solution to two-person zero-sum Markov games with an infinite horizon discounted cost criterion. We present error bounds from the optimal equilibrium value of the game when both players take “correlated” receding horizon policies that are based on exact or approximate solutions of receding finite horizon subgames. Motivated by the worst-case optimal control of queueing systems by Altman, we then analyze error bounds when the minimizer plays the (approximate) receding horizon control and the maximizer plays the worst case policy. We give two heuristic examples of the approximate receding horizon control. We extend “parallel rollout” and “hindsight optimization” into the Markov game setting within the framework of the approximate receding horizon approach and analyze their performances. From the parallel rollout approach, the minimizing player seeks to combine dynamically multiple heuristic policies in a set to improve the performances of all of the heuristic policies simultaneously under the guess that the maximizing player has chosen a fixed worst-case policy. Given $\varepsilon$>0, we give the value of the receding horizon which guarantees that the parallel rollout policy with the horizon played by the minimizer “dominates” any heuristic policy in the set by $\varepsilon$, From the hindsight optimization approach, the minimizing player makes a decision based on his expected optimal hindsight performance over a finite horizon. We finally discuss practical implementations of the receding horizon approaches via simulation and applications.

• International Journal of Control, Automation, and Systems
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• 제2권4호
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• pp.463-474
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• 2004

Game theory is a method of mathematical analysis developed to study the decision making process. In 1928, Von Neumann mathematically proved that every two-person, zero-sum game with many pure finite strategies for each player is deterministic. 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. Through the process of Darwinian selection, a population of agents can evolve to an Evolutionary Stable Strategy (ESS) as introduced by Maynard Smith in 1982. Keeping pace with these game theoretical studies, the first computer simulation of coevolution was tried out by Hillis. Moreover, Kauffman proposed the NK model to analyze coevolutionary dynamics between different species. He showed how coevolutionary phenomenon reaches static states and that these states are either Nash equilibrium or ESS in game theory. Since studies concerning coevolutionary phenomenon were initiated, there have been numerous other researchers who have developed coevolutionary algorithms. In this paper we propose a new coevolutionary algorithm named Game theory based Coevolutionary Algorithm (GCEA) and we confirm that this algorithm can be a solution of evolutionary problems by searching the ESS. To evaluate this newly designed approach, we solve several test Multiobjective Optimization Problems (MOPs). From the results of these evaluations, we confirm that evolutionary game can be embodied by the coevolutionary algorithm and analyze the optimization performance of our algorithm by comparing the performance of our algorithm with that of other evolutionary optimization algorithms.

• 한국유통학회지:유통연구
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• 제11권4호
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• pp.31-48
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• 2006

본 연구에서는 최근 이동통신단말기보조금을 둘러싸고 이동통신서비스사업자와 이동통신 단말기제조업자 사이에서 발생한 갈등상황을 중심으로 2인비영합게임을 정의하고 그에 대한 최적전략게임해를 도출하였다. 연구결과 이동통신서비스사업자와 이동통신단말기제조업자 중 자기가 속한 시장에 대한 시장지배력이 높은 사업자는 자신에게 유리한 전략으로 힘을 행사할 수 있으며, 양 사업자들이 각자의 시장에 대한 시장지배력이 비슷하게 높다면 양자간에 잠재적 갈등과 협력의 기회가 공존하고 있다는 점 등이 밝혀졌다. 또한, 본 연구의 결과는 이동통신단말기보조금에 대한 경로갈등과 유사한 다양한 제품과 서비스를 대상으로 발생될 수 있는 경로갈등의 해결을 위한 효과적인 준거기준을 제공할 수 있을 것으로 기대 된다.