• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.425-430
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• 2012

In this paper, we will prove a social equilibrium existence theorem of a generalized Nash game with affine constraint correspondences which is comparable with Nash's equilibrium existence theorem in several aspects.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.213-219
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• 2011

In this paper, we will prove an equilibrium existence theorem of a non-compact acyclic strategic game with affine constraint correspondences which is comparable with equilibrium existence theorems due to Debreu, Nash, Kim-Kum, and Lu in several aspects.

• Journal of Electrical Engineering and Technology
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• v.3 no.4
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• pp.509-513
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• 2008

In this paper, we investigate how generators' ramp-rate constraints may influence their equilibrium strategy formulation. In the market model proposed in this study, the generators' ramp-rate constraints are explicitly represented. In order to fully characterize the inter-temporal nature of the ramp-rate constraints, a dynamic game model is presented. The subgame perfect Nash equilibrium is adopted as the solution of the game and the backward induction procedure for the solution of the game is designed in this paper. The inter-temporal nature of the ramp-rate constraints results in the Markov property of the game, and we have found that the Markov property of the game significantly simplifies the subgame perfect Nash equilibrium characterization. Finally, a simple electricity market numerical illustration is presented for the successful application of the approach proposed.

• 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 of Korean Society of Transportation
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• v.23 no.4 s.82
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• pp.37-45
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• 2005

This paper presents a relationship between Nash bargaining game and Wardrop user equilibrium, which has been widely used in transportation modeling for route choice problem. Wardrop user equilibrium assumes that drivers in road network have perfect information on the traffic conditions and they choose their optimal paths without cooperation each other. In this regards, if the bargaining game process is introduced in route choice modeling, we may avoid the strong assumptions to some extent. For such purpose, this paper derives a theorem that Nash bargaining solution is equivalent to Wardrop user equilibrium as the barging process continues and prove it with some numerical examples. The model is formulated based on two-person bargaining game. and n-person game is remained for next work.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.10
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• pp.5260-5275
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• 2019

In the process of constructing the traditional offensive and defensive game theory model, these are some shortages for considering the dynamic change of security risk problem. By analysing the critical indicators of the incomplete information game theory model, incomplete information attack and defense game theory model and the mathematical engineering method for solving Bayes-Nash equilibrium, the risk-averse income function for information assets is summarized as the problem of maximising the return of the equilibrium point. To obtain the functional relationship between the optimal strategy combination of the offense and defense and the information asset security probability and risk probability. At the same time, the offensive and defensive examples are used to visually analyse and demonstrate the incomplete information game and the Harsanyi conversion method. First, the incomplete information game and the Harsanyi conversion problem is discussed through the attack and defense examples and using the game tree. Then the strategy expression of incomplete information static game and the engineering mathematics method of Bayes-Nash equilibrium are given. After that, it focuses on the offensive and defensive game problem of unsafe information network based on risk aversion. The problem of attack and defense is obtained by the issue of maximizing utility, and then the Bayes-Nash equilibrium of offense and defense game is carried out around the security risk of assets. Finally, the application model in network security penetration and defense is analyzed by designing a simulation example of attack and defense penetration. The analysis results show that the constructed income function model is feasible and practical.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.8
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• pp.2854-2874
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• 2015

This paper presents a game theoretic approach to analyze the public goods (PGs) allocation in peer-to-peer (p2p) networks. In order to reduce the free-riders and promote the cooperation among peers, we propose an incentive mechanism with cooperation-based game theory. In this paper, we regarded the contributed resources by cooperators as public goods (PGs). We also build the PGs allocation in P2P networks to be the optimization problem, and the optimal solution of PGs allocation satisfies the Bowen-Lindahl-Samuelson equilibrium. Firstly, based on the subscriber mechanism, we analyze the feasibility and prove the validity, which can achieve Nash equilibrium. However, this strategy cannot meet to Bowen-Lindahl-Samuelson equilibrium as the free-riders do not pay with their private goods for consuming the PGs. Secondly, based on the Walker mechanism, we analyze the feasibility and prove the validity for the same allocation problem, which meets to Bowen-Lindahl-Samuelson equilibrium and achieves Pareto efficiency within cooperative game. Simulations show that the proposed walker mechanism can significantly improve the network performance of throughout, and effectively alleviate free-riding problem in P2P networks.

• Journal of the Korean Operations Research and Management Science Society
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• v.38 no.4
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• pp.1-9
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• 2013

We propose a heuristic algorithm for war-game model that is appropriate for warfare in which the maneuver of the attacker is relatively certain. Our model is based on a multi-weapon extention of the Lanchester's square law. However, instead of dealing with the differential equations, we use a multi-period linear approximation which not only facilitates a solution method but also reflects discrete natures of warfare. Then our game model turns out to be a continuous game known to have an ${\varepsilon}$-Nash equilibrium for all ${\varepsilon}{\geq}0$. Therefore, our model approximates an optimal warfare strategies for both players as well as an efficient reinforcement of area defense system that guarantees a peaceful equilibrium. Finally, we report the performance of a practical best-response type heuristic for finding an ${\varepsilon}$-Nash equilibrium for a real-scale problem.

• Journal of the Korean Operations Research and Management Science Society
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• v.35 no.4
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• pp.55-79
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• 2010

This study deals with a model for platform competition in a two-sided market. We suppose there are both direct and indirect network externalities between suppliers and users of each platform. Moreover, we suppose that both users and suppliers are distributed in their relative affinity for each platform type. That is, each user [supplier] has his/her own preferential position toward each platform, and users [suppliers] are horizontally differentiated over [0, 1]. And for analytical tractability, some parameters like direct and indirect network externalities are the same across the markets. Given the parameters and the pricing profile, users and suppliers conduct subscription game, where participants select the platform that gives them the highest payoffs. This game proceeds according to a replicator dynamics of the evolutionary game, which is simplified by properly defining gains from participant's strategy in the subscription game. We find that depending on the strength of these network effects, there might either be multiple stable equilibria, at which users and suppliers distribute across both platforms, or one unstable interior equilibrium corresponding to the market tipping in favor of either platform. In both cases, we also consider the pricing power of competing platform providers under the framework of the Stackelberg game. In particular, our study examines the possible effects of the type of competition between platform providers, which may constrain the equilibrium selection in the subscription game.