• Title/Summary/Keyword: nash equilibrium

Search Result 195, Processing Time 0.031 seconds

A Linearized Transmission Model Based Market Equilibrium In Locational Pricing Environments

  • Joung, Man-Ho;Kim, Jin-Ho
    • Journal of Electrical Engineering and Technology
    • /
    • v.2 no.4
    • /
    • pp.494-499
    • /
    • 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.

Power Control Algorithm with Finite Strategies: Game Theoretic Approach (게임이론을 이용한 유한 전략 집합을 갖는 전력제어 알고리즘)

  • Kim, Ju-Hyup;Jang, Yeon-Sik;Lee, Deok-Joo;Hong, Een-Kee
    • Journal of Advanced Navigation Technology
    • /
    • v.13 no.1
    • /
    • pp.87-96
    • /
    • 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.

  • PDF

NOTE ON PURE-STRATEGY NASH EQUILIBRIA IN MATRIX GAMES

  • Ma, Weidong
    • Bulletin of the Korean Mathematical Society
    • /
    • v.49 no.6
    • /
    • pp.1251-1254
    • /
    • 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.

Bidding Strategy Determination by Defining Strategic Vector

  • Kang, Dong-Joo;Kim, Balho H.;Chung, Koo-Hyung;Moon, Young-Hwan
    • KIEE International Transactions on Power Engineering
    • /
    • v.3A no.1
    • /
    • pp.47-52
    • /
    • 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.

Estimating the Price of Anarchy Using Load Balancing Measure

  • Kim, Jae-Hoon
    • Journal of information and communication convergence engineering
    • /
    • v.7 no.2
    • /
    • pp.148-151
    • /
    • 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.

Bidding Strategy Determination by Defining Strategy Vector (전략벡터정의를 통한 입찰전략수립)

  • Kang, Dong-Joo;Moon, Young-Hwan;Oh, Tae-Kyoo;Kim, Bal-Ho
    • Proceedings of the KIEE Conference
    • /
    • 2001.11b
    • /
    • pp.60-62
    • /
    • 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.

  • PDF

A Solution Method of a Three-Player Game for Application to an Electric Power Market (전력시장 해석을 위한 3연 참여 게임의 해법 연구)

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

Game Algorithm for Power Control in Cognitive Radio Networks (전파 인지 네트워크에서 전력 제어를 위한 게임 알고리즘)

  • Rho, Chang-Bae;Halder, N.;Song, Ju-Bin
    • Journal of Advanced Navigation Technology
    • /
    • v.13 no.2
    • /
    • pp.201-207
    • /
    • 2009
  • Recently effective spectrum resource technologies have been studied using a game theorectical approach for cognitive radio networks. Radio resource management is required an effective scheme because the performance of a radio communication system much depends on it's effectiveness. In this paper, we suggest a game theoretical algorithm for adaptive power control which is required an effect scheme in cognitive radio networks. It will be a distributed network. In the network distributed cognitive radio secondary users require an adaptive power control. There are many results which are suggested some possibility of game theoretical approaches for communication resource sharing. However, we suggest a practical game algorithm to achieve Nash equilibrium of all secondary users using a Nash equilibrium theorem in this paper. Particularly, a game model was analyzed for adaptive power control of a cognitive radio network, which is involved in DSSS (Direct Sequence Spread Spectrum) techniques. In case of K=63 and N=12 in the DSSS network, the number of iteration was less than maximum 200 using the suggested algorithm.

  • PDF

Solving Mixed Strategy Nash-Cournot Equilibria under Generation and Transmission Constraints in Electricity Market

  • Lee, Kwang-Ho
    • Journal of Electrical Engineering and Technology
    • /
    • v.8 no.4
    • /
    • pp.675-685
    • /
    • 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.