Bi matrix for two power plants by different energy sources.
\\n\\n
More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
\n'}],latestNews:[{slug:"intechopen-signs-new-contract-with-cepiec-china-for-distribution-of-open-access-books-20210319",title:"IntechOpen Signs New Contract with CEPIEC, China for Distribution of Open Access Books"},{slug:"150-million-downloads-and-counting-20210316",title:"150 Million Downloads and Counting"},{slug:"intechopen-secures-indefinite-content-preservation-with-clockss-20210309",title:"IntechOpen Secures Indefinite Content Preservation with CLOCKSS"},{slug:"intechopen-expands-to-all-global-amazon-channels-with-full-catalog-of-books-20210308",title:"IntechOpen Expands to All Global Amazon Channels with Full Catalog of Books"},{slug:"stanford-university-identifies-top-2-scientists-over-1-000-are-intechopen-authors-and-editors-20210122",title:"Stanford University Identifies Top 2% Scientists, Over 1,000 are IntechOpen Authors and Editors"},{slug:"intechopen-authors-included-in-the-highly-cited-researchers-list-for-2020-20210121",title:"IntechOpen Authors Included in the Highly Cited Researchers List for 2020"},{slug:"intechopen-maintains-position-as-the-world-s-largest-oa-book-publisher-20201218",title:"IntechOpen Maintains Position as the World’s Largest OA Book Publisher"},{slug:"all-intechopen-books-available-on-perlego-20201215",title:"All IntechOpen Books Available on Perlego"}]},book:{item:{type:"book",id:"3695",leadTitle:null,fullTitle:"Supply Chain the Way to Flat Organisation",title:"Supply Chain",subtitle:"the Way to Flat Organisation",reviewType:"peer-reviewed",abstract:"With the ever-increasing levels of volatility in demand and more and more turbulent market conditions, there is a growing acceptance that individual businesses can no longer compete as stand-alone entities but rather as supply chains. Supply chain management (SCM) has been both an emergent field of practice and an academic domain to help firms satisfy customer needs more responsively with improved quality, reduction cost and higher flexibility. This book discusses some of the latest development and findings addressing a number of key areas of aspect of supply chain management, including the application and development ICT and the RFID technique in SCM, SCM modeling and control, and number of emerging trends and issues.",isbn:null,printIsbn:"978-953-7619-35-0",pdfIsbn:"978-953-51-6406-7",doi:"10.5772/105",price:139,priceEur:155,priceUsd:179,slug:"supply_chain_the_way_to_flat_organisation",numberOfPages:438,isOpenForSubmission:!1,isInWos:1,hash:null,bookSignature:"Yanfang Huo and Fu Jia",publishedDate:"January 1st 2009",coverURL:"https://cdn.intechopen.com/books/images_new/3695.jpg",numberOfDownloads:64496,numberOfWosCitations:17,numberOfCrossrefCitations:25,numberOfDimensionsCitations:38,hasAltmetrics:0,numberOfTotalCitations:80,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:null,dateEndSecondStepPublish:null,dateEndThirdStepPublish:null,dateEndFourthStepPublish:null,dateEndFifthStepPublish:null,currentStepOfPublishingProcess:1,indexedIn:"1,2,3,4,5,6,7",editedByType:"Edited by",kuFlag:!1,editors:[{id:"131846",title:"Prof.",name:"Yanfang",middleName:null,surname:"Huo",slug:"yanfang-huo",fullName:"Yanfang Huo",profilePictureURL:"https://mts.intechopen.com/storage/users/131846/images/system/131846.jpg",biography:"Education and work experience:\n2002.10-2004.10, Management science and engineering, Tianjin University, Post doctor\n2000.3-2002.9, Management science and engineering, Tianjin University, Doctor\n2004.11-now, Department of management and economy Tianjin University, Associate professor\n2008.1-2009.1, Supply chain research center in Cranfield University, UK, visiting scholar\n1994.7-1997.4, Aijin clothing company in TEDA, Operation Standard and the work quota setting\nCommittee and Memberships:\n[1] Senior member of Chinese mechanical engineering society\n[2] Member of Chinese institute of certified public accountants\n[3] Member of the branch-management and technology of the innovation methods research society of Ministry of science and technology \nResearch:\nResearch Specialty:Supply chain innovation, theory and applications of Industrial Engineering。MBA Research Specialty: Lean Production, Operations Management, Supply chain and logistics engineering。MPA Research Specialty: Performance measurement,Process management and improvement。GCT Research Specialty: Supply chain and logistics engineering, Industrial Engineering\nResearch projects:\n[1] Research on Job Standardization of “Tianji” and “Tianyu” in the second phase of construction process optimization and standardization research of Cutter suction dredger, 2010.4-2011.3\n[2] Research on Job Standardization of “Tianhu” in the first phase of construction process optimization and standardization research of Cutter suction dredger, project cooperating with enterprise, 2008.5-2009.3\n[3] Social management innovation research under the modern industrial system in Binhai new area, the development and reform commission of Binhai new area in Tianjin, 2011.1 – 2011.12\n[4] Comprehensive reform planning supporting ‘’the 12th Five-Year” guideline in Binhai new area, the office of Tianjin Binhai new area government, 2010.3 -2011.5\n[5] Research on improving the administrative efficiency in Binhai new area, the office of Tianjin Binhai new area government, 2011.1 – 2011.12\n[6] Research on supply chain coordination model and experiment based on customer behavior, National Natural Science Foundation of China(70971095)2010.1-2012.12,Number 2.\n[7] Research on innovation process coordination and performance of complex products based on lean supply chain, 20120032110035, the doctoral fund of Ministry of Education in 2012(Ph.D. supervisor class), 2013.1-2015.12. Number 2\n[8] Development and promotion of applications in enterprises of tool set of key technique and methods about management innovation, 2010IM040300, special project on national basic science and technology work (work on Innovation methods), 2010.4 -2013.4.Number 5.\n[9] Research on quality assurance methods and tools in whole life cycle of major scientific instruments project.2012IM040500, special project on national basic science and technology work (work on Innovation methods), 2012, main participant.\n[10] Hominids system management mode in Aerospace science and industry group,2005.1~2007.7,863 project(2004AA411030)Number 2.\n[11] Research on collaborative management model of space products in large types,2002.7-2004.10,863 fund (2001AA411020),Number 2.\n[12] Research on integration patterns of Enterprise logistics and information flow based on LP/TPS, Natural Science Foundation of Tianjin (023605611), 2002.6-2005.6, Number 2.\n[13] Research on empirical model of innovation networks in Research and development and transformation base in Binhai new area. soft project of Ministry of science and technology (2008GXQ6D147) 2008.8.1-2009.8.31, Number 4.\n[14] Research on integration of Production planning and scheduling based on APS/MES\n, 2005.1~2007.12, National Natural Science Foundation of China (70472063), Number 4.\nSelected publications:\n[1] Yanfang Huo, Lixiang Yang, Ying Lin. Study on Advanced Booking Discount Mode in a Two-Level Supply Chain under the Competitive Environment. Industrial Engineering and Management, 2011.16(5), 22-26.\n[2] Yanfang Huo, Xubo zhu. Regional innovation ability evaluation and dynamic optimization, Statistics and Decision, 2012(1): 59-62.\n[3] Yanfang Huo, Zhongsheng Liu. Analysis on Retailer-dominant Three-Level Supply Chain Coordination under Emergency Demand. Computer Integrated Manufacturing System——CIMS, Accepted.\n[4] Yanfang Huo, Gang Li, Fu Jia, Min Ji. Research on Petri-Net-based Eco-industrial Park Simulation of Steel Company. Journal of Tianjin University (Social Sciences), 2010, 12(1): 1-6\n[5] Yanfang Huo, Xinyue Jiang, Ershi Qi, Bingguang Li. Distributed Multi-level Modeling and Simulation of Supply Chain Integration. Industrial Engineering, 2010, 13(1): 80-84 \n[6] Yanfang Huo, Jie Wang, Bingguang Li and Binshan Lin. Modelling and Simulation of Stock-out Cost Pulled Collaborative Supply Chain Planning. International Journal of Modelling in Operations Management, Vol. 1, No. 1, 2010 \n[7] Yanfang Huo, Alan Harrison, Fu Jia, Ershi Qi. Innovation in Logistics: China-Europe Supply Chains. The Third International Conference on Operations and Supply Chain Management, Wuhan, Jul. 28 to Aug. 5, 2009(ISTP:BOP87)\n[8] Huo Yanfang, Jiang Xinyue, Wang Qianqian. Product Realization-based Performance Evaluation of Supply Chain Integration. IEEE International Conference on Management and Service Science,EMS/MASS2009, Beijing, Sep. 20-22, 2009(EI:20100212629018)\n[9] Yanfang Huo, Min Ji. APPLY TOPSIS MODEL TO EVALUATE AUTOMOTIVE LOGISTICS PERFORMANCE,ICCLTP2008, Chengdu, Oct 2008(EI:20093812323722)\n[10] Yanfang Huo, Min Ji. Apply Quality Function Deployment Method to Manage Logistics Quality. ICCLTP2008, Chengdu, Oct 2008 (EI:20093812323721)\n[11] Yanfang Huo, Xinyue Jiang. Research on CPFR and Warehousing Management. 2007 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2007, p 4640-4643 (EI 080311028293) \n[12] Yanfang Huo,Ershi Qi, Xu Gang, et al. Study on service styles and payoff pattern of listed park companies. 2006 IEEE International Conference on Service Operations and Logistics, and Informatics, SOLI 2006, p 664-668 (EI 074610921145)\n[13] Yanfang Huo, Ershi Qi, Yang Wang, Wenming Cheng. Study on the Integrated Development Model of Complex Product Systems Based on Virtual Organizations. Manufacturing Technology and Machine, 2004, (9): 46-49\n[14] Yanfang Huo, Ershi Qi. Integrated Model of TPS/ERP and Supported Technology for Chinese Manufacturing Industry. Industrial Engineering, 2004, 7(4): 1-5\n[15] Yanfang Huo, Ershi Qi. Application of QFD Method in the Process of MRP-Oriented Logistics Systems Optimization. Industrial Engineering ,2003,6(5): 21-25\n[16] Yanfang Huo, Chuanming Liu, Ling Wang. Module Designing of Knowledge Management Applications in Virtual enterprise. Research and Development Management, 2004, 16(3):58-61\n[17] Ershi Qi, Yanfang Huo. Research on the Development Strategy of China's Industrial Engineering Based on the Process of Industrialization. Chinese Journal of Mechanical Engineering, 2004, 40(10):6-9, EI Search 04538760182\n[18] Ershi Qi, Huo Yanfang. Study of Solution and Suggestion on the Implementation of CIMS Project. Chinese Journal of Mechanical Engineering (English). 2000.13(Supplement). EI 01015493589\n[19] Ershi Qi, Huo Yanfang. Development Overview of Industrial Engineering in Chinese Mainland. Chinese Journal of Industrial Engineering (Tai).2002,19(2):1-8,EI Search 05389370715\n[20] Rohit Verma,Kenneth K. Boyer (writer). Yanfang Huo, Bingguang Li, Gang Xu(translated). Operations and Supply Chain Management: World-class Theory and Practice. Beijing: Tsinghua University Press, 2010.7 \n[21] Yanfang Huo, Fu Jia. Supply chain, the way to flat organisation. Published by In-Tech. Vienna, Austria, 2008.12\n[22] Ershi Qi, Huo Yanfang etc. Industrial Engineering and Management. Published by the Press of Science, Beijing, 2011\n[23] Ershi Qi, Huo Yanfang etc. Public Performance Management and Methods. Published by Tianjin University Press,Tianjin, 2011\n[24] Ershi Qi, Huo Yanfang, Liang Liu. Logistics Engineering and Management Introduction, Published by Tsinghua University Press,Beijing, 2009\n[25] Bingguang Li, Yanfang Huo, Gang Xu(translated). (Canada)Arnold.Tony etc(writed). Introduction to Materials Management. Published by Tsinghua University Press, Beijing, 2008.7 \n[26] Bingguang Li, Yanfang Huo(translated). APICS Dictionary(the 11th Edition). Printed by APICS Association, 2008.7",institutionString:null,position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"1",institution:{name:"Tianjin University",institutionURL:null,country:{name:"China"}}}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,coeditorOne:{id:"252218",title:"Dr.",name:"Fu",middleName:null,surname:"Jia",slug:"fu-jia",fullName:"Fu Jia",profilePictureURL:"https://mts.intechopen.com/storage/users/252218/images/system/252218.jpg",biography:"Dr Jeff (Fu) Jia is a Reader in Supply Chain Management at EFM, University of Bristol. Dr Jia is a visiting professor to Zhejiang University, China and Free University of Bozen-Bolzano (FUB), Italy. 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He is a productive author publishing in international conferences and top OM/SCM, IB and agri-food journals such as International Journal of Operations and Production Management, Supply Chain Management: An International Journal, International Journal of Production Economics, Food Policy, International Business Review, Technological Forecasting and Social Change, Journal of Business Logistics, Journal of Cleaner Production, Journal of Purchasing and Supply Management, and International Journal of Logistics Management among others. He has also co-authored three books and contributed several book chapters. Dr Jia is an Associate Editor of International Journal of Operations and Production Management (ABS 4) and Journal of Purchasing and Supply Management and a Managing Editor of International Food and Agribusiness Management Review (IFAMR) and an Editorial Review Board Memeber of Industrial Marketing Management. 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In recent years, many researchers have developed models to discuss the importance of lowering carbon emissions and its potential impact on society by examining economic growth, international trade, and health benefits. Khan et al. [1] examined the relationship between green logistics indices, economic, environmental, and social factors through the perspective of Asian emerging economies. By adopting a Fully Modified OLS (FMOLS) Model and Dynamic OLS (DOLS) they claimed that logistics operations, particularly the efficiency of customs clearance processes, quality of logistics services and trade and transport-related infrastructure are positively and significantly correlated with per capita income, manufacturing value added and trade openness, whereas greater logistics operations are negatively associated with social and environmental problems including, climate change, global warming, carbon emissions, and poisoning atmosphere. Khan et al. [2] examined the potential relationship between public health expenditures, logistics performance indices, renewable energy, and ecological sustainability in members of the Association of Southeast Asian Nations by applying the structural equation modeling approach. They showed that the use of renewable energy in logistics operations will improve environmental and economic performance to reduce emissions, whereas environmental performance is negatively correlated with public health expenditures, indicating that greater environmental sustainability can improve human health and economic growth. In [3], economic growth and environmental sustainability in the South Asian Association for Regional Cooperation using the data from the South Asian Association for Regional Cooperation (SAARC) member countries from 2005 to 2017 was examined. Adopting the panel autoregressive distributed lag technique to examine the hypotheses, they find that environmental sustainability is strongly and positively associated with national scale-level green practices, including renewable energy, regulatory pressure, eco-friendly policies, and the sustainable use of natural resources. In [4], the consumption of renewable energy with international trade and environmental quality in Nordic countries from 2001 to 2018 is investigated. Their findings concluded that renewable energy is strongly and positively associated with international trade in Nordic countries. Furthermore, [5] adopted multi-criteria-decision-making techniques to examine barriers in the sustainable supply chain management (SSCM) when firms are facing heavy pressure to adopt green practices in their supply chain (SC) operations to achieve better socio-environmental sustainability.
Around the world governments, businesses and individuals have committed to reducing carbon emission. As a result, the energy economy is highly exposed to these processes. As industries push for renewable energies, technology will need to step in to ensure reliability of the power supply. Therefore, there remains a need for exploiting the role of hybrid technology, its dynamics, limitations on the reduction of pollution levels and policy implementation within the wider carbon emissions debate. This is due to the vital role hybrid technology plays in energy production processes and the ability for the energy system to offer a better energy security. Development of such lower carbon emission policies has potential benefits to the environment and ecological sustainability to those economies. However, within many of these environmental policy models, technology is incorporated as an exogenous variable and limited attention is given to endogenous technology, other technological breakthroughs, potential government subsidies or collaborative innovations to integrate low carbon technology in environmental economics. Such interventions will promote the renewable energy sector to use natural resources and undertake public-private partnership investments to minimize dependence on fossil fuel derived energy.
To investigate the effects of hybrid-enabling technology when producing energy to meet consumption demand, we assume energy producing firms follow the Bertrand game paradigm. In the presence of government subsidy for the development and sustainability of renewable energy, tax on pollution created by energy producing firms will motivate them to undertake Research & Development (R&D) measures to improve hybrid enabling technologies to further reduce the level of carbon pollution. As a result, from an economic point of view it is an interesting question to examine the Bertrand-Nash equilibrium under such a dynamic environment. This chapter examines this concept via a Stochastic Differential game paradigm.
Many researchers have applied game theory to study carbon reduction behavior in electricity markets. In [6], the Cournot equilibria in an oligopolistic electricity market subject to a linear demand function is examined. In [7], the power suppliers bidding behavior is evaluated under the supply function equilibrium (SFE) paradigm, where the market power of an independent system operator (ISO) is modeled as a bi-level multi-objective problem. In [8], the equilibrium strategies in random-demand procurement auctions in the electricity market is obtained and presented a method for explicit calculation of the bid strategies is presented. [9] proposed a Nash bargaining game model to examine how governments can determine the taxes and subsidies in a competitive electricity market whilst achieving their environmental objectives. In [10, 11, 12, 13, 14], the role of government as a leading player who intervenes in competitive electricity markets to promote environmental protection is evaluated. In [15], the role of government, when managing environmental sustainability in a complete electricity market in a Stackelberg game paradigm is examined. In [16], a more robust trans-boundary industrial pollution reduction strategy for global emission collaborations is presented. The dynamics of each country’s quantity of pollution is modeled as a Brownian motion with Jumps to capture the systematic jumps caused by surprise effects arising from policy uncertainties within the economy. However, a crucial limitation within many of these environmental policy models, is that technological change is incorporated as an exogenous variable and does not consider the role of endogenous hybrid-enabling technology or other technological breakthroughs, hence limiting the dynamics of these models.
We quantify an optimal level of subsidy for the sharing of hybrid-enabling technology in an energy market under a Bertrand-duopoly game. We formulate a Stochastic Differential Game (SDG) to analyze the stability of the Stackelberg, Nash and cooperative equilibria via a feedback control strategy. We then adopt limit expectation and variance of the improvement degree to identify the influence of external environment limitations on the decision maker. We show that the game depends on its parameters and the equilibria chosen. We consider an electricity market composed of power plants I and II, with each one having the choice between fossil fuels
In this model, we consider a Bertrand duopoly game for two power plants under endogenous hybrid-enabling technology. In the first stage the matrix of prices
stochastic endogenous hybrid-enabling technology innovation is introduced into a two-player stochastic differential game with random interference factors, which capture uncertain external environment factors and the internal limitations within the shared hybrid-enabling technology decision process. In doing so, we provide a framework to quantify the impacts of market power on prices.
we show that both power plants invest in R&D measures and that the limit of expectation and variance of the improvement degree can be applied to identify the influence of random factors.
mathematically, we show that the issue of the game depends on the parameters of the game and the type of equilibrium one considers.
by applying the HJB equation we obtain the optimal effort level and the optimal level of subsidy for sharing hybrid-enabling technology via feedback equilibrium strategies whilst examining the Stackelberg equilibria, Nash equilibria and cooperative equilibria under Bertrand duopoly.
we reveal that for a given level of payoff distribution the Stackelberg equilibria under endogenous hybrid-technology innovation and the sharing paradigm dominate the Nash equilibria.
we show that in Stackelberg and Nash games, optimal hybrid-enabling technology innovation is proportional to the government subsidy, but the variance improvement degree of the Stackelberg game is different to the results of the Nash game.
our characterization of the short run price competition by strategic supplies for renewable and fossil resources, provides a more robust model than that presented by Bertrand-Edgworth, in which price competition with fixed (endogenous) capacities was used.
our model shows that robust cost-reducing R&D investments with effective hybrid-enabling technology innovation strengthens an innovator’s competitive position and the Stackelberg structure emerges as an equilibrium outcome, allowing each power plant to optimally use energy sources to produce electricity while maximizing their payoffs.
Therefore, under a Stochastic Differential Game (SDG) paradigm with uncertainty, each power plant can optimally use energy sources to produce electricity while maximizing their payoffs. Each power plant is capable of using fossil fuels
In recent years, researchers have incorporated the theory of SDGs, originated from [14, 17, 18, 19, 20] to analyzed environmental issues. Especially [21] analyzed (two player) zero-sum stochastic differential games in a rigorous way, and proved that the upper and lower value functions of such games satisfy the dynamic programming principle whilst being the unique viscosity solutions of their associated Hamilton-Jacobi-Bellman-Isaacs equations.
In Section 2, the proposed model and elements of evolutionary game theory are presented. In Section 3 by implementing the Stackelberg game we examine feedback Stackelberg equilibria, optimal level of subsidy for the shared hybrid-enabling technology from its counterpart and the limit of expectation and variance. In Section 4 by implementing a Nash game we examine feedback Nash equilibria and the limit of expectation and variance under hybrid-enabling technology. In Section 5 by implementing a cooperative game we examine feedback equilibria and the limit of expectation and variance under hybrid-enabling technology. In Section 6, comparative analysis of equilibrium results are described. Section 7 concludes the study. Appendix at the end of the chapter contains proofs.
We propose that the production process of electricity leads to emissions and is proportional to the power industry’s use of energy source. We assume that there are two power plants (Player I) and (Player II) in the energy market and each power plant is capable of using
Under the theory of evolutionary games, the production strategies in the
Then each iteration of an evolutionary game, where two matched power plants in accordance with Bertrand paradigm compete with each market and play a one-shot non-zero-sum game, represents the benchmark game of the population. If
We define the continuous demand function
where
The government’s tariff policy for the power plants with respect to their source of energy for long-time periods are transparent, and this information is available to the public. Therefore, it is assumed that the competitive power plants follow the government’s financial legislation, having the capability and technological skills to produce electricity from specific sources at any given time to meet energy demand. Then for each time-period the power plant will consider the tariff-rate quota or feed-in-tariff and adopt a pricing strategy for the selected energy source. Hence, we conclude that the production rate of the power plants is equal to the corresponding demand rates with a negligible internal consumption and waste rate.
To apply the Backward induction technique to investigate the equilibrium prices, demand, and profits, we define the profit function for each power plant as
where
Defining
Simultaneously solving Eq. (4), obtain
such that
where
Restricting ourselves to a two matched symmetric two-person bi- matrix game in random contest in a one-population evolutionary game, we define the payoff (utility) in Table 1.
Production Strategy | Fossil Fuel | Renewable Sources | |
Fossil Fuel | |||
Renewable Sources |
Bi matrix for two power plants by different energy sources.
Then via equation
Obviously the bimatrix of the power plant II, is given by:
The probability that player I choosing row 1 is
The probability that player II choosing row 1 is
Then the value of the game for Player I is
and the value of the game for Player II is
Suppose (
Otherwise Player I can change
Similarly, for
Otherwise Player II can change y slightly and do better. It follows that the unique Nash equilibrium (
Both players will undertake R&D measures on hybrid-enabling technology to ensure immediate reliability and affordability in energy production whilst reducing GHG-emissions. We assume that the strategic effects implemented by power plant I (Player I), has improved hybrid-enabling technology to generate energy and utilize energy sources in a much efficient way. This gives a superior advantage to power plant I overpower plant II (Player II) and both power plants are rational to maximize their profits. Although Power plant II has heterogeneous resources to hybrid-enabling technology, from a practical point of view it is logical for power plant I to share this technology with power plant II, because the price competition is typically characterized by a second-mover advantage. Many researchers have investigated the effects of these commitments in Cournot, Bertrand and Stackelberg setups. See [29, 30, 31]. Due to the government incentives, tariff-rate quota, feed-in-tariff and R&D incentive measures, the power companies will be competitive to improve their efficiency. Let
and
where
Let
Let
where
The first inequality says that each demand is downward sloping in own price, and the second that goods are substitutes (each demand increases with the price of the other good). [32] shows that in case of symmetric firms, there is a second-mover (first-mover) advantage for both players when each profit function is strictly concave in own action and strictly increasing (decreasing) in rival’s action, and reaction curves are upward (downward) sloping.
Then a sufficient condition on the super-modularity of the profit function is obtained via the profit function
where
We further assume that the total revenue is allocated between two players and
and
where
Theory of strong Stackelberg reasoning is an improved version of an earlier theory [35], which provides an explanation of coordination in all dyadic (two-player) common interest games. It provides an explanation of why players tend to choose strategies associated with a payoff-dominant Nash equilibrium. Its distinctive assumption is that players behave as though their co-players will anticipate any strategy choice and invariably choose a best reply to it. Stackelberg strategies resulting from this form of reasoning do not form Nash equilibria. The theory makes no predictions, because a non-equilibrium outcome is inherently unstable, leaving at least one player with a reason to choose differently and thereby achieve a better payoff. Strong Stackelberg reasoning is a simple theory, according to which players in dyadic games choose strategies that would maximize their own payoffs if their co-players could invariably anticipate their strategy choices and play counter-strategies that yield the maximum payoffs for themselves. The key assumption is relatively innocuous, first because game theory imposes no constraints on players’ beliefs, apart from consistency requirements, and second because the theory does not assume that players necessarily believe that their strategies will be anticipated, merely that they behave as though that is the case, as a heuristic aid to choosing the best strategy. Strong Stackelberg reasoning is, in fact, merely a generalization of the minorant and majorant models introduced by [36] and used to rationalize their solution of strictly competitive games.
To promote the sharing of hybrid-enabling technology, the Player II (the leader) determine an optimal sharing effort sharing level and an optimal subsidy scheme. Then the Player I (the follower) choose his/her optimal sharing level according to the optimal sharing effort level and subsidy. This leads to a Stackelberg equilibrium.
where
where
Via the first order conditions, we obtain the optimal values
where
Substituting the results of Eqs. (37) and (38) into Eq. (39), obtain
Via the first order conditions of (Eq. (40)), we obtain the optimal values
And the optimal value for
and
Hence, the solution of the HJB equation is an unary function with
and simplifying (Eq. (40)), obtain:
This implies that,
where
and
Substituting the results of
The payoff of Player I and Player II, under the Stackelberg game paradigm is related to the improvement degree of hybrid-enabling technology via Proposition 4. To analyze the limit of expectations and variance under Stackelberg game equilibrium rewrite (Eq. (19)) as follows.
where
and
Then
Solving the above non-homogeneous linear differential equation, will obtain the results.
Under Nash-non-cooperative game setting, Player I and Player II simultaneously and independently choose their optimal efforts levels of heterogeneous hybrid-enabling technology sharing concept to maximize their profits.
where
where
where
Poof of Proposition 8 is like the derivation of Proposition 6.
Under cooperative game paradigm, Player I and Player II will choose to collaborate/share their hybrid-enabling technology development knowledge while sharing the payoff function in order to maximize their total payoffs. As a result, hybrid-enabling technology can be improved through this effort as well.
and the optimal cooperative payoff function under hybrid-enabling technology on renewable sources and on fossil fuel, respectively.
where
Then the optimal revenue sharing function satisfies the following HJB equation
Via the first order conditions, now obtain the optimal values
Substituting the results of Eqs. (69) and (70), obtain
Hence, the solution of the HJB equation is an unary function with
Substituting the results of Eqs. (72) and (73), into
where
and
(ii) Player I will prefer to participate in a cooperative game over a non-cooperative game with Player II under the condition such that
and
(iii) The total payoff for Player I under a Stackelberg game exceeds the total payoff of Nash non-cooperative game with Player II under the condition such that
and
(iv). Player II will prefer to participate in a cooperative game over a non-cooperative game with Player I under the condition such that
and
and
In this chapter a complete study of an energy market by considering a Bertrand duopoly game with two power plants using endogenous hybrid-enabling technology was presented. Numerous game paradigms were articulated and defined including Stackelberg, Nash non-cooperative and cooperative games as well as their relevant equilibria via a feedback control strategy. Mathematically, the necessary conditions under which a power plant will move from taking part in a non-cooperative Nash game to participate as a leader in a Stackelberg game was derived. In doing so, this model allowed us to quantify the optimal level of subsidy for sharing the hybrid-enabling technology. We then adopted the concept of limit expectation and variance of the improvement degree to identify the influence of random factors of external environment and limitations of the decision maker. It is found that for a given level of payoff distribution the Stackelberg equilibria with technological enhancements, the knowledge sharing paradigm dominates the Nash equilibria. In both Stackelberg and Nash games, optimal technological enhancements for power plants were found to be proportional to the government subsidy, but the variance improvement degree of the Stackelberg game differed to the results of the Nash non-cooperative game due to the influence of random factors.
Furthermore, we have shown that due to optimal price reaction functions being upward sloping, the subsidy level plays a decisive role on the payoff function of power plant II as the leader in a Stackelberg game. This model shows that cost reducing R&D investments with efficient hybrid-enabling technology innovation/s strengthens one’s competitive bargaining position via the level of subsidy for Power Plant I to become a follower in the Stackelberg game. By analyzing this stochastic differential game model, we capture the government subsidy incentive as well as the subsidy that the leader (Power Plant II) pays the follower (Power Plant I) to share hybrid-enabling technology.
The proposed quantitative framework could assist policymakers when determining the appropriate R&D incentives for the development of hybrid-enabling technology within the energy market to achieve desired short and long-term environmental objectives with respect to budget limitations and environmental considerations.
Via the first order conditions, first obtain the optimal values
where
Substituting Eqs. (A.2) and (A.3) results to Eq. (A.4) and via the first order conditions, we obtain the optimal values
Hence, the solution of the HJB equation is an unary function with
where
and
Substituting
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\n\nOur end-to-end publishing service frees our authors and editors to focus on what matters: research. We empower them to shape their fields and connect with the global scientific community.
\n\n"In developing countries until now, advancement in science has been very limited, because insufficient economic resources are dedicated to science and education. These limitations are more marked when the scientists are women. In order to develop science in the poorest countries and decrease the gender gap that exists in scientific fields, Open Access networks like IntechOpen are essential. Free access to scientific research could contribute to ameliorating difficult life conditions and breaking down barriers." Marquidia Pacheco, National Institute for Nuclear Research (ININ), Mexico
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