• Title, Summary, Keyword: Mixed strategy

### Solving Mixed Strategy Equilibria of Multi-Player Games with a Transmission Congestion (다자게임 전력시장에서 송전선 혼잡시의 복합전략 내쉬균형 계산)

• Lee, Kwang-Ho
• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.11
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• pp.492-497
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• 2006
• Nash Equilibrium (NE) is essential to investigate a participant's bidding strategy in a competitive electricity market. The transmission line constraints make it difficult to compute the NE due to causing a mixed strategy NE instead of a pure strategy NE. Computing a mixed strategy is more complicated in a multi-player game. The competition among multi-participants is modeled by a two-level hierarchical optimization problem. A mathematical programming approach is widely used in finding this equilibrium. However, there are difficulties to solving a mixed strategy NE. This paper presents two propositions to add heuristics to the mathematical programming method. The propositions are based on empirical studies on mixed strategies in numerous sample systems. Based on the propositions a new formulation is provided with a set of linear and nonlinear equations, and an algorithm is suggested for using the prepositions and the newly-formulated equations.

### Leader-Follower Model Analysis on Mixed Strategy Nash Equilibrium of Electricity Market with Transmission Congestion (송전선 혼잡시의 복합전략 내쉬균형에 대한 선도-추종자 모형 해석)

• Lee, Kwang-Ho
• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.2
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• pp.187-193
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• 2012
• Nash Equilibrium (NE) is as useful tool for investigating a participant's strategic generation quantity in a competitive electricity market. Cournot model may give a mixed strategy NE instead of a pure strategy when transmission constraints are considered. A mixed strategy is difficult to compute, complicated to understand conceptually, and hard to implement in an electricity market practically. This paper presents that a mixed strategy does not appear in Stackelberg leader-follower model even under a transmission congestion. A solution method is proposed for the leader-follower model under a nondifferentiable space of a strategy variable. Based on the pure strategy NE with a transmission line congested, the merit of leader-follower model is shown from a social welfare point of view.

### Effect of Financial Transmission Rights on the Strategic Bidding Behavior of the Electricity Producers (재무적 송전권이 발전사의 전략적 입찰에 미치는 영향)

• Lee, Kwang-Ho;Shin, Jae-Hong
• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.7
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• pp.1226-1231
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• 2010
• This paper looks at the influence of Financial Transmission Rights (FTRs) on the market value(Social Welfare; SW) in the competitive electricity market. The transmission line constraints make it difficult to compute the Nash Equilibrium (NE) due to causing a mixed strategy NE instead of a pure strategy NE. Computing a mixed strategy is more complicated in a multi-player game. The aim of this paper are to compute a mixed strategy NE and analyze SW in power transaction with FTRs. This paper introduces a formula and a technique for solving NE of multi-player game with FTRs. In addition, it analyzes the influence of holding of FTRs by generation company on SW and it proposes the SW at NE is influenced by Power Transfer Distribution Factor (PTDF) where holder of FTRs are located. The assertion is verified by calculating the mixed strategy utilizing the Cournot model widely used for studies on FTRs.

### Strategy Equilibrium in Stackelberg Model with Transmission Congestion in Electricity Market

• Lee, Kwang-Ho
• Journal of Electrical Engineering and Technology
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• v.9 no.1
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• pp.90-97
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• 2014
• Nash Cournot Equilibrium (NCE) has been widely used in a competitive electricity market to analyze generation firms' strategic production quantities. Congestion on a transmission network may lead to a mixed strategy NCE. Mixed strategy is complicated to understand, difficult to compute, and hard to implement in practical market. However, Stackelberg model based equilibrium does not have any mixed strategy, even under congestion in a transmission line. A guide to understanding mixed strategy equilibrium is given by analyzing a cycling phenomenon in the players' best choices. This paper connects the concept of leader-follower in Stackelberg model with relations between generation firms on both sides of the congested line. From the viewpoint of social welfare, the surplus analysis is presented for comparison between the NCE and the Stackelberg equilibrium (SE).

### Effect of Generation Capacity Constraints on a Mixed Strategy Nash Equilibrium in a Multi-Player Game (다자게임에서 발전력제약이 복합전략 내쉬균형에 미치는 영향)

• Lee, Kwang-Ho
• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.1
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• pp.34-39
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• 2008
• Nash Equilibrium(NE) is essential to investigate a participant's bidding strategy in a competitive electricity market. Congestion on a transmission line makes it difficult to compute the NE due to causing a mixed strategy. In order to compute the NE of a multi-player game, some heuristics are proposed with concepts of a key player and power transfer distribution factor in other studies. However, generation capacity constraints are not considered and make it more difficult to compute the NE in the heuristics approach. This paper addresses an effect of generation capacity limits on the NE, and suggest a solution technique for the mixed strategy NE including generation capacity constraints as two heuristic rules. It is reported in this paper that a role of the key player who controls congestion in a NE can be transferred to other player depending on the generation capacity of the key player. The suggested heuristic rules are verified to compute the mixed strategy NE with a consideration of generation capacity constraints, and the effect of the generation constraints on the mixed strategy NE is analyzed in simulations of IEEE 30 bus systems.

### 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.

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

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

### Weighting objectives strategy in multicriterion fuzzy mechanical and structural optimization

• Shih, C.J.;Yu, K.C.
• Structural Engineering and Mechanics
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• v.3 no.4
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• pp.373-382
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• 1995
• The weighting strategy has received a great attention and has been widely applied to multicriterion optimization. This gaper examines a global criterion method (GCM) with the weighting objectives strategy in fuzzy structural engineering problems. Fuzziness of those problems are in their design goals, constraints and variables. Most of the constraints are originated from analysis of engineering mechanics. The GCM is verified to be equivalent to fuzzy goal programming via a truss design. Continued and mixed discrete variable spaces are presented and examined using a fuzzy global criterion method (FGCM). In the design process a weighting parameter with fuzzy information is introduced into the design and decision making. We use a uniform machine-tool spindle as an illustrative example in continuous design space. Fuzzy multicriterion optimization in mixed design space is illustrated by the design of mechanical spring stacks. Results show that weighting strategy in FGCM can generate both the best compromise solution and a set of Pareto solutions in fuzzy environment. Weighting technique with fuzziness provides a more relaxed design domain, which increases the satisfying degree of a compromise solution or improves the final design.

### 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
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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.

### The Impact of the Knowledge Management Strategic Alignment on the Innovation of Manufacturing Firms (기업전략과 지식경영 전략의 연계가 제조기업의 혁신에 미치는 영향)

• Choe, Jong-Min
• Journal of the Korean Operations Research and Management Science Society
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• v.36 no.2
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• pp.67-88
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• 2011
• This study empirically investigated the effects of knowledge management(KM) strategic alignment on the KM activities as well as the product and process innovation of manufacturing firms. Based on the framework, which employs the usage levels of target costing systems(TCS) and information technology(IT) infrastructure, four types of KM strategies were identified and proposed：mixed, explorative, exploitative and negative strategies. In this research, these four types of KM strategies were empirically validated. According to the results of this study, it was found that when a explorative KM strategy is aligned with a low-cost strategy, KM activities are activated and the degree of a process innovation is increased. It was observed that in the case of the alignment between a differentiation strategy and a exploitative KM strategy, both KM activities and the level of a product innovation are enhanced. The results also demonstrated that for the enhancement of both a process and a product innovation through the activation of KM activities, a mixed KM strategy must be aligned with a composite business strategy, which focuses on a low-cost as well as a differentiation strategies. Accordingly, it is concluded that the KM activities and the levels of the product and process innovation can be activated or improved with the alignment of the KM strategies and business strategies.