• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.8
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• pp.2854-2874
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• 2015

This paper presents a game theoretic approach to analyze the public goods (PGs) allocation in peer-to-peer (p2p) networks. In order to reduce the free-riders and promote the cooperation among peers, we propose an incentive mechanism with cooperation-based game theory. In this paper, we regarded the contributed resources by cooperators as public goods (PGs). We also build the PGs allocation in P2P networks to be the optimization problem, and the optimal solution of PGs allocation satisfies the Bowen-Lindahl-Samuelson equilibrium. Firstly, based on the subscriber mechanism, we analyze the feasibility and prove the validity, which can achieve Nash equilibrium. However, this strategy cannot meet to Bowen-Lindahl-Samuelson equilibrium as the free-riders do not pay with their private goods for consuming the PGs. Secondly, based on the Walker mechanism, we analyze the feasibility and prove the validity for the same allocation problem, which meets to Bowen-Lindahl-Samuelson equilibrium and achieves Pareto efficiency within cooperative game. Simulations show that the proposed walker mechanism can significantly improve the network performance of throughout, and effectively alleviate free-riding problem in P2P networks.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1992.04b
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• pp.403-412
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• 1992

This note examines a situation where a risk-neutral insurer and a risk-averse individual (prospective insured) negotiate to reach an arbitration point of the price of insurance over the terms of an insurance contract in order to maximize their respective self-interests. The situation is modeled as a Nash bargaining problem. We analyze the dependence of the price of insurance, which is determined by the Nash solution, on the parameters such as the size of insured loss, the probability of a loss, the degree of risk-aversion of the insured, and the riskiness of loss distribution.

• Proceedings of the KIEE Conference
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• 2002.07a
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• pp.380-382
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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 of imperfect competition of a deregulated electricity system the key task is to find the Nash equilibrium. In this paper, the bimatrix approach for finding Nash equilibria in electricity markets is investigated. This approach determines pure and mixed equilibria using the complementarity pivot algorithm. The mixed equilibrium in the matrix approach has the equal number of non-zero property. This property makes it difficult to reproduce a smooth continuous distribution for the mixed equilibrium. This paper proposes an algorithm for adjusting the quantization value of discretization to reconstruct a continuous distribution from a discrete one.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.9
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• pp.392-398
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• 2006

Maintenance scheduling of generating units (MSU) has strategic dimension in an oligopolistic market. Strategic MSU of gencos can affect a market power through capacity withdrawal which is related to bidding strategy in an generation wholesale market. This paper presents a combined framework that models the interrelation between competitive bidding and strategic MSU. The combined game model is represented as some sub-optimization problems of a market operator (MO) and gencos, that should be solved through bi-level optimization scheme. The gradient method with dual variables is also adopted to calculate a Nash Equilibrium (NE) by an iterative update technique in this paper. Illustrative numerical example shows that NE of a supply function equilibrium is obtained properly by using proposed solution technique. The MSU made by MO is compared with that by each genco and that under perfect competition market.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.5
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• pp.214-219
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• 2006

Oligopoly differs from perfect competition and monopoly in that a firm must consider rival firms' behavior to determine its own best policy. This interrelationship among firms is the issue examined in this paper. In the oligopoly market, the complete information market means that each producer has full information about itself, the market, and its rivals. That is, each producer knows the market demand function, its own cost function and the cost functions of rivals. On the other hand, the incomplete information market means that in general each producer lacks full information about the market or its rivals. Here, we assume that each firm doesn't know the cost functions and the strategic biddings of its rivals. The main purpose of this paper is to analyze firm' strategic behaviors and equilibrium in an electricity market with incomplete information. In the case study, the complete information market and the incomplete market are compared at the Nash Equilibrium from the viewpoints of market price, transaction quantities, consumer benefits, and Social Welfare.

• 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.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.3
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• pp.1028-1046
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• 2022

Genome-wide association studies (GWAS) aim to find the significant genetic variants for common complex disease. However, genotype data has privacy information such as disease status and identity, which make data sharing and research difficult. Differential privacy is widely used in the privacy protection of data sharing. The current differential privacy approach in GWAS pays no attention to raw data but to statistical data, and doesn't achieve equilibrium between utility and privacy, so that data sharing is hindered and it hampers the development of genomics. To share data more securely, we propose a differential privacy preserving approach of data sharing for GWAS, and achieve the equilibrium between privacy and data utility. Firstly, a reasonable disturbance interval for the genotype is calculated based on the expected utility. Secondly, based on the interval, we get the Nash equilibrium point between utility and privacy. Finally, based on the equilibrium point, the original genotype matrix is perturbed with differential privacy, and the corresponding random genotype matrix is obtained. We theoretically and experimentally show that the method satisfies expected privacy protection and utility. This method provides engineering guidance for protecting GWAS data privacy.

• Proceedings of the KIEE Conference
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• 2003.07a
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• pp.639-642
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• 2003

This paper presents a method for evaluating the mixed nash equilibria of the Cournot model for N-Gencos. in wholesale electricity market. In the wholesale electricity market, the strategies of N-Genco. can be applied to the game model under the conditions which the Gencos. determine their stratgies to maximize their benefit. Generally, the Lemke algorithm is evaluated the mixed nash equlibria in the two-player game model. However, the necessary condition for the mixed equlibria of N-player are modified as the necessary condition of N-1 player by analyzing the Lemke algorithms. Although reducing the necessary condition for N-player as the one of N-1 player, it is difficult to and the mixed nash equilibria participated two more players by using the mathmatical approaches since those have the nonlinear characteristics. To overcome the above problem, this paper presents the generalized necessary condition for N-player and proposed the object function to and the mixed nash equlibrium. Also, to evaluate the mixed equilibrium through the nonlinear objective function, the Particle Swarm Optimization (PSO) as one of the heuristic algorithm are proposed in this paper. To present the mixed equlibria for the strategy of N-Gencos. through the proposed necessry condition and the evaluation approach, this paper proposes the mixed equilibrium in the cournot game model for 3-players.