• Journal of the Korea Society for Simulation
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• v.27 no.1
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• pp.39-49
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• 2018

An SLBM (submarine-launched ballistic missile) seriously threatens the national security due to its stealthiness that makes it difficult to detect in advance. We consider a destroyer deployment optimization problem for effectively detecting an SLBM. An optimization model is based on the two-person zero-sum game in which an adversary determines the firing and arriving places with an appropriate trajectory that provides a low detection probability, and we establish a destroyer deployment plan that guarantees the possibly highest detection probability. The proposed two-person zero-sum game model can be solved with the corresponding linear programming model, and we perform computational studies with a randomly generated area and scenario and show the optimal mixed strategies for both the players in the game.

• Journal of the military operations research society of Korea
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• v.31 no.1
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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

• Journal of the Korean Operations Research and Management Science Society
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• v.6 no.1
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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.

• Journal of the military operations research society of Korea
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• v.8 no.2
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• pp.57-68
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• 1982

Bimatrix games are the two-person non-zero-sum non-cooperative games. These games were studied by Mills, Lemke, Howson, Millham, Winkels, and others. This paper is a systematic and synthetic survey relevant to bimatrix games. Among the many aspects of researches on bimatrix games, emphasis in this paper is placed on the relation of the equilibrium set to Nash subsets. Topics discussed are as follows: Properties of equilibrium point; The structure of equilibrium set; Relation of Nash subsets to equilibrium set; Algorithm for finding the equilibrium points; Concepts of solutions on bimatrix games.

• Journal of the Korean Operations Research and Management Science Society
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• v.6 no.2
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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.

• Journal of the Korean Operations Research and Management Science Society
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• v.7 no.2
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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.

• Korean Management Science Review
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• v.26 no.1
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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.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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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.

• Journal of Korea Game Society
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• v.1 no.1
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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.

• Journal of Distribution Research
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• v.11 no.4
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• pp.31-48
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• 2006

This study was motivated by a recent channel conflict on subsidies for mobile handset between a service provider and a handset manufacturer in the mobile communication market. In this study, we have developed a two-person non-zero sum game for the channel conflict on subsidies for mobile handset, and derived its optimal strategic game solution. As a result, we have found that, between the service operator and the handset manufacturer, one who has high level of market leadership in his own market has a power to affect the optimal strategic game solution. We have also found that, when the service operator and the handset manufacturer have relatively high level of market leadership in their own market, there exist both of potential channel conflict and cooperation. The result of this study may provide an effective reference for a solution of similar channel conflicts.