• 대한교통학회지
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• 제23권4호
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• pp.37-45
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• 2005

본 연구는 Nash의 협력게임인 협상게임(bargaining game)과 Wardrop의 사용자 균형해와의 관계를 규명하는 데 목적이 있다. Wardrop의 균형은 다수의 운전자들이 교통상황을 정확히 알고 있고(perfect information), 동시에 합리적으로 경로를 선택(rationality)한다는 경직된 가정이 존재하는데, 이는 실제로 존재하는 운전자 상호간의 교류나 타협을 배제하고 있다. 이런 측면에서 운전자간의 교류와 조절과정을 Nash게임의 협상과정(bargaining process)으로 표현할 경우, Wardrop의 경직된 기본가정들을 어느 정도 완화할 수 있을 것으로 보인다. 이를 위하여 본 연구에서는 Nash의 협상게임에 대한 교통망측면의 검토와 Nash의 협상해(bargaining solution)가 Wardrop의 사용자 균형(user equilibrium)과 동일함을 정리(theorem)를 통하여 증명하고 몇 가지 예제로 이를 확인한다. 협상게임은 대표적인 2인 협조게임(two-person cooperative game)으로 본 연구에서도 주로 2인 게임에 대해서 기술하며, 향후 n-인게임(n-person game) 모형에 대해서는 간략히 언급토록 한다.

• Journal of Electrical Engineering and Technology
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• 제3권4호
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• pp.509-513
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• 2008

In this paper, we investigate how generators' ramp-rate constraints may influence their equilibrium strategy formulation. In the market model proposed in this study, the generators' ramp-rate constraints are explicitly represented. In order to fully characterize the inter-temporal nature of the ramp-rate constraints, a dynamic game model is presented. The subgame perfect Nash equilibrium is adopted as the solution of the game and the backward induction procedure for the solution of the game is designed in this paper. The inter-temporal nature of the ramp-rate constraints results in the Markov property of the game, and we have found that the Markov property of the game significantly simplifies the subgame perfect Nash equilibrium characterization. Finally, a simple electricity market numerical illustration is presented for the successful application of the approach proposed.

• 경영과학
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• 제26권1호
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• pp.1-5
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• 2009

I study a solution concept which preserves the nice Nash equilibrium properties of two-person zero-sum games, and define a locally competitive equilibrium which is characterized by a saddle point with respect to the coordinates of strategies. I show that a locally competitive equilibrium shares the properties of uniqueness of equilibrium payoffs, interchangeablity of equilibrium strategies and convexity of the equilibrium set.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제5권3호
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• pp.542-559
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• 2011

Most game-theoretic works of Aloha have emphasized investigating Nash equilibria according to the system state represented by the number of network users and their decisions. In contrast, we focus on the possible change of nodes' utility state represented by delay constraint and decreasing utility over time. These foregone changes of nodes' state are more likely to instigate selfish behaviors in networking environments. For such environment, in this paper, we propose a repeated Bayesian slotted Aloha game model to analyze the selfish behavior of impatient users. We prove the existence of Nash equilibrium mathematically and empirically. The proposed model enables any type of transmission probability sequence to achieve Nash equilibrium without degrading its optimal throughput. Those Nash equilibria can be used as a solution concept to thwart the selfish behaviors of nodes and ensure the system stability.

• 한국경영과학회지
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• 제14권2호
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• pp.97-104
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• 1989

This paper extends the existence proofs of a Nash equilibrium to a more general class of differentila game models with constraints on the control spaces. With the assumptions of continuity, convexity, and compactness, the existence is proved using Kakutani Theorem and via a path-following approach. Furthermore, the proof for a period-by-period optimization of multi-period problems provides an insight to a numerical solution algorithm to differential game models with constraints.

• 대한전기학회논문지:전력기술부문A
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• 제52권6호
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• pp.340-346
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• 2003

This paper presents a game theory application for an analysis of uniform price auction in a simplified competitive electricity market and analyzes the properties of Nash equilibrium for various conditions. We have assumed that each generation firm submits his bid to a market in the form of a sealed bid and the market is operated as a uniform price auction. Two firms are supposed to be the players of the market, and we consider the maximum generation quantity constraint of one firm only. The system demand is assumed to have a linear relationship with market clearing prices and the bidding curve of each firm, representing the price at which he has a willingness to sell his generation quantity, is also assumed to have a linear function. In this paper, we analyze the effects of maximum generation quantity constraints on the Nash equilibrium of the uniform price auction. A simple numerical example with two generation firms is demonstrated to show the basic idea of the proposed methodology.

• 한국경영과학회지
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• 제38권4호
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• pp.1-9
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• 2013

We propose a heuristic algorithm for war-game model that is appropriate for warfare in which the maneuver of the attacker is relatively certain. Our model is based on a multi-weapon extention of the Lanchester's square law. However, instead of dealing with the differential equations, we use a multi-period linear approximation which not only facilitates a solution method but also reflects discrete natures of warfare. Then our game model turns out to be a continuous game known to have an ${\varepsilon}$-Nash equilibrium for all ${\varepsilon}{\geq}0$. Therefore, our model approximates an optimal warfare strategies for both players as well as an efficient reinforcement of area defense system that guarantees a peaceful equilibrium. Finally, we report the performance of a practical best-response type heuristic for finding an ${\varepsilon}$-Nash equilibrium for a real-scale problem.

• KIEE International Transactions on Power Engineering
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• 제5A권1호
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• pp.85-92
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• 2005

In this paper, Nash equilibriums of generation markets are investigated using a game theory application for simplified competitive electricity markets. We analyze the characteristics of equilibrium states in N-company spot markets modeled by uniform pricing auctions and propose a new method for obtaining Nash equilibriums of the auction. We assume that spot markets are operated as uniform pricing auctions and that each generation company submits its bids into the auction in the form of a seal-bid. Depending on the bids of generation companies, market demands are allocated to each company accordingly. The uniform pricing auction in this analysis can be formulated as a non-cooperative and static game in which generation companies correspond to players of the game. The coefficient of the bidding function of company-n is the strategy of player-n (company-n) and the payoff of player-n is defined as its profit from the uniform price auction. The solution of this game can be obtained using the concept of the non-cooperative equilibrium originating from the Nash idea. Based on the so called residual demand curve, we can derive the best response function of each generation company in the uniform pricing auction with N companies, analytically. Finally, we present an efficient means to obtain all the possible equilibrium set pairs and to examine their feasibilities as Nash equilibriums. A simple numerical example with three generation companies is demonstrated to illustrate the basic idea of the proposed methodology. From this, we can see the applicability of the proposed method to the real-world problem, even though further future analysis is required.

• 전기학회논문지
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• 제61권2호
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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.

• 환경정책연구
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• 제6권3호
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• pp.91-114
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• 2007

Song and Nagaki(2007)에 나타나 있는 것과 같은 동북아지역의 황사(먼지모래폭풍: DSS) 저감을 위한 비음부담 공조체제는 참여국의 협정불이행으로 실행가능성에 문제가 제기된다. 만일 비협조적 전략이 각국에게 보다 현실적이 라면, 내쉬균형이 실현가능한 비용분담 게임의 결과를 예측하게 하여줄 수 있다. 본 연구에 따르면, 연속전략게임의 경우, ADB의 황사저감사업의 비용이 각국 투자에 의해 조달된다는 가정하에 무한한 내쉬균형이 발견된다. 또한, 비연속전략은 3각형 평면으로 나타나는 연속전략의 내쉬균형의 꼭짓점으로 나타나게 되며, 공조적 게임의 결과는 무한한 균형 점들을 1개의 점으로 수렴하게 된다.