• Title, Summary, Keyword: Nash equilibrium

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BEST PROXIMITY PAIRS AND NASH EQUILIBRIUM PAIRS

  • Kim, Won-Kyu;Kum, Sang-Ho
    • Journal of the Korean Mathematical Society
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    • v.45 no.5
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    • pp.1297-1310
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    • 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.

Approach for Evaluating the Nash Equilibrium of Cournot Game Model for N-Gencos by Using Payoff Matrix in Wholesale Electricity Market (도매전력시장에서 N-발전사업자의 보수행렬을 이용한 꾸르노 모델의 내쉬균형점 도출을 위한 방법론)

  • Park Jong-Bae;Lim Jung-Youl;Lee Ki-Song;Shin Joong-Rin
    • 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.

Analysis of the Influence of Transmission Capacity on the Electricity Market Equilibrium (송전용량이 전력시장 균형에 미치는 영향해석)

  • Nam, Young-Woo
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.23 no.2
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    • pp.182-189
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    • 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.

Mixed Strategy of Nash Equilibrium in Power Transaction With Constraints (전력거래에서 제약조건이 고려된 내쉬 균형점의 복합전략 연구)

  • Lee, Gwang-Ho
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.51 no.4
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    • pp.196-201
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    • 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.

WEIGHT NASH EQUILIBRIA FOR GENERALIZED MULTIOBJECTIVE GAMES

  • Kim, Won Kyu
    • Journal of the Chungcheong Mathematical Society
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    • v.13 no.1
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    • pp.13-20
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    • 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.

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Alternating Offers Bargaining Game and Wardrop's User Equilibrium (Nash의 협상게임과 Wardrop의 사용자 균형)

  • Lim, Yong-Taek
    • Journal of Korean Society of Transportation
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    • v.23 no.4
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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.

ON GENERALIZED WEIGHT NASH EQUILIBRIA FOR GENERALIZED MULTIOBJECTIVE GAMES

  • Kim, Won-Kyu;Ding, Xie-Ping
    • Journal of the Korean Mathematical Society
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    • v.40 no.5
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    • pp.883-899
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    • 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.

Equilibrium of Voluntary Agreements on Recycling Wastes (폐기물재활용에 있어서 자발적 협약의 균형)

  • Park, June-Woo
    • Journal of Environmental Policy
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    • v.5 no.4
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    • pp.107-126
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    • 2006
  • The voluntary agreement between industries and government on the recycling of wastes has been analysed. The agreement is one of the threatened voluntary agreements. Theoretically these agreements make it possible to fulfill recycling goals with minimized cost. It is the objective of this paper to evaluate the efficiency of the voluntary agreement on recycling wastes by examining of Nash Equilibrium. In the first place, the equilibrium of a bilateral agreement between the representative of industries (association of firms) and government will be analysed to confirm if cost minimization strategies by the association result in a sub-game perfect Nash Equilibrium. This is followed by an analysis of a multilateral agreement among the members of the association to see how the equilibrium and efficiency conditions change. We tried to find some implications that the result of the analysis casts on the environmental policy matters.

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