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

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

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.54 no.2
• /
• pp.97-106
• /
• 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 the Korean Institute of Illuminating and Electrical Installation Engineers
• /
• v.23 no.2
• /
• pp.182-189
• /
• 2009

Nash equilibrium is usually used to investigate a generator's strategic bidding in electricity markets. Some literatures show that the transmission constraints may induce no pure strategy equilibrium and make it hard to find the equilibrium. Using an analytical approach to find a mixed strategy Nash equilibrium in electricity market with transmission constraints, we analyze the influence of transmission capacity on the mixed strategy Nash equilibrium. Finally, a simple numerical example is provided to support the claims of this paper.

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

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

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.51 no.4
• /
• pp.196-201
• /
• 2002

An important aspect of the study of power system markets involves the assessment of strategic behavior of participants for maximizing their profits. In models for imperfect competition of a deregulated system, the key tack is to find the Nash equilibrium. When the constraints are not considered in the power market, the equilibrium has the form of a pure strategy. However, the constraints are considered, the equilibrium has the form of a mired strategy. In this paper the bimatrix game approach leer finding a mixed equilibrium is analyzed. The Nash equilibrium of a mixed strategy will be used adequately for the analysis of market power.

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

• Journal of the Korean Mathematical Society
• /
• v.40 no.5
• /
• pp.883-899
• /
• 2003

In this paper, we will introduce the general concepts of generalized multiobjective game, generalized weight Nash equilibria and generalized Pareto equilibria. Next using the fixed point theorems due to Idzik [5] and Kim-Tan [6] , we shall prove the existence theorems of generalized weight Nash equilibria under general hypotheses. And as applications of generalized weight Nash equilibria, we shall prove the existence of generalized Pareto equilibria in non-compact generalized multiobjective game.

• Journal of the Chungcheong Mathematical Society
• /
• v.13 no.1
• /
• pp.13-20
• /
• 2000

The purpose of this paper is to give a new existence theorem of a generalized weight Nash equilibrium for generalized multiobjective games by using the quasi-variational inequality due to Yuan.