• Journal of Electrical Engineering and Technology
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• 제2권4호
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• pp.494-499
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• 2007

In this paper, we have investigated how transmission network constraints can be modeled in an electricity market equilibrium model. Under Cournot competition assumption, a game model is set up considering transmission line capacity constraints. Based on locational marginal pricing principle, market clearing is formulated as a total consumers# benefit maximization problem, and then converted to a conventional optimal power flow (OPF) formulation with a linearized transmission model. Using market clearing formulation, best response analysis is formulated and, finally, Nash equilibrium is formulated. In order for illustration, a numerical study for a four node system with two generating firms and two loads are presented.

• 한국항행학회논문지
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• 제13권1호
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• pp.87-96
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• 2009

본 논문에서는 무선통신에서 유한개의 전략집합을 갖는 전력제어 문제를 게임이론을 통하여 분석하였다. 기존의 게임이론을 이용한 전력제어에서는 개방루프 제어에서와 같이 초기전송 전력을 결정하는 연속적인 게임 모델에 국한된 반면, 본 논문에서는 폐루프 전력제어에서와 정해진 전력제어 step size 만큼 전력을 올리거나 내리는 전력제어 문제를 게임 이론의 전형적인 모델 중의 하나인 죄수 딜레마 모형을 이용하여 분석하였다. 분석결과 전력을 올리는 전략이 내쉬 균형임을 증명하였고, 따라서 이와 같은 상황에서는 모든 단말기가 자신의 전력을 향상시키려고 시도하기 때문에 전체 시스템 측면에서는 효율적이지 못하다. 본 논문에서는 인접 셀 간 간섭이 심각한 환경에서 효율적인 전력제어 알고리즘을 구현하기 위하여 게임모형의 효용함수를 새롭게 정의하였고, 그 결과 모든 단말이 자신의 효용함수를 최대화 하려고 노력한다고 하더라도 자신의 송신 전력이 일정한 수준으로 유지될 수 있는 알고리즘을 개발하였다.

• 대한수학회보
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• 제49권6호
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• pp.1251-1254
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• 2012

Pure-strategy Nash Equilibrium (NE) is one of the most important concepts in game theory. Tae-Hwan Yoon and O-Hun Kwon gave a "sufficient condition" for the existence of pure-strategy NEs in matrix games [5]. They also claimed that the condition was necessary for the existence of pure-strategy NEs in undominated matrix games. In this short note, we show that these claims are not true by giving two examples.

• KIEE International Transactions on Power Engineering
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• 제3A권1호
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• pp.47-52
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• 2003

This paper presents a schematic process based on the method of eliminating dominated strategies to obtain the optimal bidding strategy Pursuing the Nash equilibrium Point. The Proposed approach is demonstrated for a bidding game in a generation competitive market with 2-dimensional bidding strategy vectors constituting a price-quantity strategy curve.

• Journal of information and communication convergence engineering
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• 제7권2호
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• pp.148-151
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• 2009

We consider the problem of optimizing the performance of a system with resources shared by non-cooperative users. The worst-cast ratio between the cost of a Nash equilibrium and the optimal cost, called Price of Anarchy, is investigated. It measures the performance degradation due to the users' selfish behavior. As the objective function of the optimization problem, we are concerned in a load balancing measure, which is different from that used in the previous works. Also we consider the Stackelberg scheduling which can assign a fraction of the users to resources while the remaining users are free to act in a selfish manner.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 추계학술대회 논문집 전력기술부문
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• pp.60-62
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• 2001

This paper shows the optimal bidding strategy determination method using Nash equilibrium concept by defining bidding strategy vector. This vector is 2-dimension vector whose components are generation amount and generation cost. Thereby we are able to make all possible strategies and their's payoff table. And then we erase dominated strategies one by one so that we obtain Nash equilibrium, the optimal bidding strategy of generation bidding game.

• 충청수학회지
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• 제34권2호
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• pp.109-117
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• 2021

In this paper, as an application of a multivalued generalization of the Németh fixed point theorem, we will prove a new existence theorem of Nash equilibrium for a generalized game 𝓖 = (X_i; A_i, P_i)_i∈I with geodesic convex values in Hadamard manifolds.

• 대한전기학회논문지:전력기술부문A
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• 제52권6호
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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.

• 한국항행학회논문지
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• 제13권2호
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• pp.201-207
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• 2009

게임 이론을 적용한 기술은 전파 인지 시스템에서 전파 자원을 효율적으로 이용할 수 있는 유용한 방법으로 그 연구가 활발히 진행되고 있다. 전파 자원 관리 시스템은 그 효율성에 따라서 전파 통신 시스템의 성능을 좌우하게 되므로 효율적인 알고리즘의 연구가 요구된다. 본 논문에서는 이러한 분산 전력 제어가 적응적으로 구현되도록 하기 위하여 게임 이론을 적용한 새로운 시도를 해석적으로 제안하였다. 기존의 연구 결과들은 전력 제어를 게임 이론적으로 해석하는 가능성만을 보인 반면, 본 논문에서는 전파 인지 네트워크에서 네쉬 균형 (Nash Equilibrium)을 구하는 구체적인 알고리즘을 제안하였다. 네트워크에 접속된 부사용자들이 공동으로 만족하는 네쉬 균형 즉, 최적 전력 제어를 달성하도록 하는 방법을 제안하였다. 특히, 전파 인지 네트워크가 DSSS (Direct Sequence Spread Spectrum) 기술을 사용할 경우를 가정하여 이에 대한 적응적 전력 제어를 위한 게임 이론적 모델을 적용하였다. 게임 이론적인 알고리즘을 적용한 결과 DSSS 네트워크에서 K=63이고 N=12인 경우 네쉬 균형에 도달하기 위한 반복 횟수가 최대 200 이하인 결과를 보였다.

• Journal of Electrical Engineering and Technology
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• 제8권4호
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• pp.675-685
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• 2013

Generation capacities and transmission line constraints in a competitive electricity market make it troublesome to compute Nash Equilibrium (NE) for analyzing participants' strategic generation quantities. The NE can cause a mixed strategy NE rather than a pure strategy NE resulting in a more complicated computation of NE, especially in a multiplayer game. A two-level hierarchical optimization problem is used to model competition among multiple participants. There are difficulties in using a mathematical programming approach to solve a mixed strategy NE. This paper presents heuristics applied to the mathematical programming method for dealing with the constraints on generation capacities and transmission line flows. A new formulation based on the heuristics is provided with a set of linear and nonlinear equations, and an algorithm is suggested for using the heuristics and the newly-formulated equations.