• Proceedings of the KIEE Conference
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• 2005.07a
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• pp.775-777
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• 2005

In this paper, effects of the subsidy in the electricity market on the market equilibrium are analyzed. The generation competition markets are considered as the basic market structure. The market equilibrium with Cournot game model is derived, first. Then, the variation of Nash equilibrium is investigated when the subsidies to generation companies are provided. The market equilibrium with the subsidy in the electricity market, which is equivalent to the subgame perfect equilibrium, is analytically derived using Stackelberg game model and backward induction method. From this, how the provisions of subsidy to generation companies can affect the strategic behaviors of the generation companies and corresponding market equilibrium are explored, in this paper. Numerical examples are provided to illustrate the basic idea of this paper.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.225-234
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• 2013

Many studies of experimental economics have produced outcomes which contradict the predictions of Nash equilibrium, which relies heavily upon the premise of selfishness of an individual. In the games involving contexts of social conflicts represented by the prisoners' dilemma game, the experiments yields outcomes quite different from what are predicted by the conventional wisdom. In order to fill this gap between the conventional Nash Equilibrium and experimental outcomes, non-selfish (or other-regarding) motives of human behavior are introduced and then a new equilibrium concept, RAE-equilibrium is developed. It is also proved that an RAE-equilibrium exists under quite general conditions. Then it is applied to the prisoners' dilemma game that some of the experimental outcomes can be explained.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.29-35
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• 2010

In this note, we will prove a new equilibrium existence theorem for a compact acyclic strategic game by using Begle's fixed point theorem.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.149-156
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• 1996

We discuss sensitivity of equilibrium points in bimatrix games depending on small variances (perturbations) of data. Applying implicit function theorem to a linear complementarity problem which is equivalent to the bimatrix game we investigate sensitivity of equi-librium points with respect to the perturbation of parameters in the game. Namely we provide the calculation of equilibrium points deriva-tives with respect to the parameters.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.367-377
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• 2014

In this paper, we first introduce a generalized concept of Berge strong equilibrium for a generalized game $\mathcal{G}=(X_i;T_i,f_i)_{i{\in}I}$ of normal form, and using a fixed point theorem for compact acyclic maps in admissible convex sets, we establish the existence theorem of generalized Berge strong equilibrium for the game $\mathcal{G}$ with acyclic values. Also, we have demonstrated by examples that our new approach is useful to produce generalized Berge strong equilibria.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.52 no.6
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• pp.347-353
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• 2003

In models of imperfect competition of deregulated electricity markets, the key task is to find the Nash equilibrium(NE). The approaches for finding the NE have had two major bottlenecks: computation of mixed strategy equilibrium and treatment of multi-player games. This paper proposes a payoff matrix approach that resolves these bottlenecks. The proposed method can efficiently find a mixed strategy equilibrium in a multi-player game. The formulation of the m condition for a three-player game is introduced and a basic computation scheme of solving nonlinear equalities and checking inequalities is proposed. In order to relieve the inevitable burden of searching the subspace of payoffs, several techniques are adopted in this paper. Two example application problems arising from electricity markets and involving a Cournot and a Bertrand model, respectively, are investigated for verifying the proposed method.

• Journal of Korean Institute of Industrial Engineers
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• v.22 no.2
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• pp.189-207
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• 1996

In this paper, a market share competition model for two firms with asymmetric conditions is considered with. In the model, the asymmetry between two firms is given by the difference of market shares In the existing market and the change of market share is supposed to be occurred only through pioneering a new market. Since the timing decision of market pioneering is based on the continuous time domain, a super game structure which has infinitely many numbers of subgames is employed for the modeling. In the course of equilibrium finding, we show that there exists no subgame-perfect pure strategy equilibrium In this game. So, we apply a mixed strategy concept and find a unique subgame-perfect equilibrium behavior strategy. As a result of equilibrium analysis, we know that the relative sizes of pioneering Incentives between two firms are varying with parameter conditions. However, the global speed of market pioneering is proven to be independent with the level of asymmetry between two firms.

• Journal of Advanced Navigation Technology
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• v.13 no.1
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• pp.87-96
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• 2009

The purpose of this paper is to analyze the power control problem in wireless communications with game theoretic approach. The major contribution of the present paper is that we formulated the problem as a game with a finite number of strategies while most of the previous game theoretic power control literatures modeled with continuous game in which there are infinite number of strategies. It should be noted that the closed-loop power control would be performed in a discrete manner, power up or down from the present level of power with fixed power control step size. We model the current closed-loop power control scheme with the famous Prisoner's dilemma model and show that the power-up strategy is Nash equilibrium. That is, every mobile tries to increase their power and approach to their maximal power. Thus, the outcome of current power control (Nash equilibrium) is inefficient. In order to attain efficient power control for the environment where ICI(Inter-Cell Interference is severe, we developed a new payoff function in which the penalty mechanism is introduced and derived conditions under which power-down becomes Nash equilibrium strategy for all players. Furthermore we examined the trajectory of equilibrium power when the power control game will be played repeatedly.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.52 no.9
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• pp.542-549
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• 2003

In this paper, a novel approach to generator maintenance scheduling strategy in competitive electricity markets based on non-cooperative dynamic game theory is presented. The main contribution of this study can be considered to develop a game-theoretic framework for analyzing strategic behaviors of generating companies (Gencos) from the standpoints of the generator maintenance-scheduling problem (GMP) game. To obtain the equilibrium solution for the GMP game, the GMP problem is formulated as a dynamic non-cooperative game with complete information. In the proposed game, the players correspond to the profit-maximizing individual Gencos, and the payoff of each player is defined as the profits from the energy market. The optimal maintenance schedule is defined by subgame perfect equilibrium of the game. Numerical results for two-Genco system by both proposed method and conventional one are used to demonstrate that 1) the proposed framework can be successfully applied in analyzing the strategic behaviors of each Genco in changed markets and 2) both methods show considerably different results in terms of market stability or system reliability. The result indicates that generator maintenance scheduling strategy is one of the crucial strategic decision-makings whereby Gencos can maximize their profits in a competitive market environment.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.52 no.11
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• pp.668-674
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• 2003

The electric marketplace is in the midst of major changes designed to promote competition. No longer vertically integrated with guaranteed customers and suppliers, electric generators and distributors will have to compete to sell and buy electricity. Unit commitment (UC) in such a competitive environment is not the same as the traditional one anymore. The objective of UC is not to minimize production cost as before but to find the solution that produces a maximum profit for a generation firm. This paper presents a hi-level formulation that decomposes the UC game into a generation-decision game (first level game) and a state(on/off)-decision game (second level game). Derivation that the first-level game has a pure Cournot Nash equilibrium(NE) helps to solve the second-level game. In case of having a mixed NE in the second-level game, this paper chooses a pure strategy having maximum probability in the mixed strategy in order to obviate the probabilistic on/off state which may be infeasible. Simulation results shows that proposed method gives the adequate UC solutions corresponding to a NE.