• Title/Summary/Keyword: Mixed equilibrium problem

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A Cloud-Edge Collaborative Computing Task Scheduling and Resource Allocation Algorithm for Energy Internet Environment

  • Song, Xin;Wang, Yue;Xie, Zhigang;Xia, Lin
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.15 no.6
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    • pp.2282-2303
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    • 2021
  • To solve the problems of heavy computing load and system transmission pressure in energy internet (EI), we establish a three-tier cloud-edge integrated EI network based on a cloud-edge collaborative computing to achieve the tradeoff between energy consumption and the system delay. A joint optimization problem for resource allocation and task offloading in the threetier cloud-edge integrated EI network is formulated to minimize the total system cost under the constraints of the task scheduling binary variables of each sensor node, the maximum uplink transmit power of each sensor node, the limited computation capability of the sensor node and the maximum computation resource of each edge server, which is a Mixed Integer Non-linear Programming (MINLP) problem. To solve the problem, we propose a joint task offloading and resource allocation algorithm (JTOARA), which is decomposed into three subproblems including the uplink transmission power allocation sub-problem, the computation resource allocation sub-problem, and the offloading scheme selection subproblem. Then, the power allocation of each sensor node is achieved by bisection search algorithm, which has a fast convergence. While the computation resource allocation is derived by line optimization method and convex optimization theory. Finally, to achieve the optimal task offloading, we propose a cloud-edge collaborative computation offloading schemes based on game theory and prove the existence of Nash Equilibrium. The simulation results demonstrate that our proposed algorithm can improve output performance as comparing with the conventional algorithms, and its performance is close to the that of the enumerative algorithm.

Typical Consideration On The Basic Model of Decision Making (의사결정의 기본 MODEL에 관한 유형적 고찰)

  • 김면성
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.6 no.9
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    • pp.111-124
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    • 1983
  • The basic model of decision problem the enterprise is conforonted with includes the following 3 elements ; 1) Elements that can not be controlled by the decision maker : In the thesis elements are named environmental variables, and varied itself according to the change of environmental condition. 2) Elements that can be controlled by the decision maker ; These elements are called decision elements in the thesis and variable according to the event. 3) object of decision making : The degree of achievement to the object is identified by taking various criteria- The index indicating the degree of achievement to the object whatever criterion is applied is called object function in the thesis. It's the fanetion of environmental variable, decision variable and object function. The relation between them brings forth the relation formula that characterize the each problem. The basic types of decision making model use in the thesis are as following ; 1) The problem of decision making under conditions of certainty. 2) The problem of decision making under conditions of risk. 3) The problem of decision making under conditions of uncertainty. 4) The problem of decision making under competitive condition. in general case that the Profit of two decision makers varies, what we regard the decision that make the sum of profit of two men maximum as the best choice for two men has a reasonability in certain case. When the sum of profit two men is zero, by taking toe promise that ail of them art according to the min-max criteria and by extending the object of choice to the mixed strategy. We certify the existance of equilibrium solution and admit them as the best solution of competitive model in general.

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Optimal ESS Investment Strategies for Energy Arbitrage by Market Structures and Participants

  • Lee, Ho Chul;Kim, Hyeongig;Yoon, Yong Tae
    • Journal of Electrical Engineering and Technology
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    • v.13 no.1
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    • pp.51-59
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    • 2018
  • Despite the advantages of energy arbitrage using energy storage systems (ESSs), the high cost of ESSs has not attracted storage owners for the arbitrage. However, as the costs of ESS have decreased and the price volatility of the electricity market has increased, many studies have been conducted on energy arbitrage using ESSs. In this study, the existing two-period model is modified in consideration of the ESS cost and risk-free contracts. Optimal investment strategies that maximize the sum of external effects caused by price changes and arbitrage profits are formulated by market participants. The optimal amounts of ESS investment for three types of investors in three different market structures are determined with game theory, and strategies in the form of the mixed-complementarity problem are solved by using the PATH solver of GAMS. Results show that when all market participants can participate in investment simultaneously, only customers invest in ESSs, which means that customers can obtain market power by operating their ESSs. Attracting other types of ESS investors, such as merchant storage owners and producers, to mitigate market power can be achieved by increasing risk-free contracts.

Dynamic Limit and Predatory Pricing Under Uncertainty (불확실성하(不確實性下)의 동태적(動態的) 진입제한(進入制限) 및 약탈가격(掠奪價格) 책정(策定))

  • Yoo, Yoon-ha
    • KDI Journal of Economic Policy
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    • v.13 no.1
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    • pp.151-166
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    • 1991
  • In this paper, a simple game-theoretic entry deterrence model is developed that integrates both limit pricing and predatory pricing. While there have been extensive studies which have dealt with predation and limit pricing separately, no study so far has analyzed these closely related practices in a unified framework. Treating each practice as if it were an independent phenomenon is, of course, an analytical necessity to abstract from complex realities. However, welfare analysis based on such a model may give misleading policy implications. By analyzing limit and predatory pricing within a single framework, this paper attempts to shed some light on the effects of interactions between these two frequently cited tactics of entry deterrence. Another distinctive feature of the paper is that limit and predatory pricing emerge, in equilibrium, as rational, profit maximizing strategies in the model. Until recently, the only conclusion from formal analyses of predatory pricing was that predation is unlikely to take place if every economic agent is assumed to be rational. This conclusion rests upon the argument that predation is costly; that is, it inflicts more losses upon the predator than upon the rival producer, and, therefore, is unlikely to succeed in driving out the rival, who understands that the price cutting, if it ever takes place, must be temporary. Recently several attempts have been made to overcome this modelling difficulty by Kreps and Wilson, Milgram and Roberts, Benoit, Fudenberg and Tirole, and Roberts. With the exception of Roberts, however, these studies, though successful in preserving the rationality of players, still share one serious weakness in that they resort to ad hoc, external constraints in order to generate profit maximizing predation. The present paper uses a highly stylized model of Cournot duopoly and derives the equilibrium predatory strategy without invoking external constraints except the assumption of asymmetrically distributed information. The underlying intuition behind the model can be summarized as follows. Imagine a firm that is considering entry into a monopolist's market but is uncertain about the incumbent firm's cost structure. If the monopolist has low cost, the rival would rather not enter because it would be difficult to compete with an efficient, low-cost firm. If the monopolist has high costs, however, the rival will definitely enter the market because it can make positive profits. In this situation, if the incumbent firm unwittingly produces its monopoly output, the entrant can infer the nature of the monopolist's cost by observing the monopolist's price. Knowing this, the high cost monopolist increases its output level up to what would have been produced by a low cost firm in an effort to conceal its cost condition. This constitutes limit pricing. The same logic applies when there is a rival competitor in the market. Producing a high cost duopoly output is self-revealing and thus to be avoided. Therefore, the firm chooses to produce the low cost duopoly output, consequently inflicting losses to the entrant or rival producer, thus acting in a predatory manner. The policy implications of the analysis are rather mixed. Contrary to the widely accepted hypothesis that predation is, at best, a negative sum game, and thus, a strategy that is unlikely to be played from the outset, this paper concludes that predation can be real occurence by showing that it can arise as an effective profit maximizing strategy. This conclusion alone may imply that the government can play a role in increasing the consumer welfare, say, by banning predation or limit pricing. However, the problem is that it is rather difficult to ascribe any welfare losses to these kinds of entry deterring practices. This difficulty arises from the fact that if the same practices have been adopted by a low cost firm, they could not be called entry-deterring. Moreover, the high cost incumbent in the model is doing exactly what the low cost firm would have done to keep the market to itself. All in all, this paper suggests that a government injunction of limit and predatory pricing should be applied with great care, evaluating each case on its own basis. Hasty generalization may work to the detriment, rather than the enhancement of consumer welfare.

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