基于期权博弈理论的R&D投资决策研究
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摘要
研究与开发(R&D)是企业获得核心竞争力的基础,是企业长期发展战略的重要组成部分。对R&D项目进行定量评价时,以净现值法为基础的传统投资决策方法忽略了投资项目的不确定性、投资时机的可延迟性、成本的不可逆性和竞争等许多重要因素,采取“要么现在投资,要么永远不投资”的刚性投资模式,使企业丧失许多宝贵的投资机会和成长空间。因此,在不确定的竞争环境下,科学地选择R&D投资时机成为企业R&D成功的关键。期权博弈理论不是对传统投资决策方法的否定,是在其基础上结合实物期权理论和博弈论,形成的新的科学决策方法。本文在传统投资决策理论的基础上,将实物期权理论与博弈论有机结合,应用实物期权理论评估R&D项目的期权价值,解决R&D投资的不可逆性、不确定性和灵活性问题,利用博弈论分析竞争者之间的交互作用,判断可能存在的均衡形式以及发生均衡的条件,构建R&D投资决策的期权博弈模型,确定企业R&D投资的最优时机和最优策略。
对R&D投资决策的基本理论进行回顾和评述。分析传统R&D投资决策方法及其局限性,论述实物期权理论处理R&D投资过程中不确定性的优势,剖析R&D投资的期权特性和博弈特性。在此基础上,建立期权博弈理论在R&D投资决策中的应用框架,从企业的竞争地位和竞争者的战略反应两个角度,分析R&D投资策略选择模式以及R&D投资中的先动优势和劣势,识别R&D投资的不确定性及其对项目价值的影响,对不确定性进行数学描述,进一步从期权博弈的角度明确R&D投资项目价值构成,为构建期权博弈定价模型奠定理论基础。
运用实物期权定价、动态规划和仿真方法,针对R&D投资时机和策略选择,构造市场不确定条件下和技术不确定条件下的R&D投资决策的期权博弈模型。在市场不确定条件下,考虑突发事件具有随机性以及参与R&D竞争的企业的不同质性,假定随机市场需求符合带跳的几何布朗运动,R&D初始投资成本和经营成本均不相同,构建不对称的双寡头垄断的连续期权博弈模型,得到跟随者、领先者、同时投资者的价值函数和投资临界点,分析突发事件和投资成本对投资临界点的影响,讨论三种均衡策略的发生形式和条件。分析表明:跟随者投资临界值对经营成本的变化更敏感,而领先者投资临界值对初始投资成本的变动更敏感;瞬时波动率和突发事件都能导致投资临界值的增加,但是对跟随者投资临界值的影响更显著;企业最优投资均衡策略取决于竞争双方的成本差异和先动优势。
在Weeds的技术不确定模型基础上,假设企业间R&D能力和投入成本均不对称,构建技术不确定条件下的期权博弈模型,得到跟随者、领先者和同时投资者的价值函数和投资临界值,重点分析企业自身R&D能力及竞争者的R&D能力对投资临界值的影响。结果表明:企业自身R&D能力的增强可以降低投资临界值,竞争对手R&D能力的增强将提高投资临界值,而且都是对跟随者投资临界值的影响更显著。对不对称双寡头垄断企业的投资策略进行分析,得到不同于前人的均衡结果,指出仍然可能存在序贯均衡,用数值释例和仿真方法验证序贯均衡的存在。
For an enterprise, research and development (R&D) is the basis of its core competence, and also an important component of its long-term development strategy. In the quantitative assessment of R&D projects, conventional means of investment decision making, generally based on net present value, neglects some significant factors, including the uncertainty of investment projects, the allowable delay of vestment time, the non-reversible of costs, and competitive. Such problems result in hard-mode strategy of investment, which always is“now or never”. This will give rise to lose of investment opportunities as well as room to grow. Thus, it is evident that scientific identification of investment time plays a key role in R&D activities on the condition of uncertain competitive environment. Option game theory is not a complete negation of conventional investment decision-making method, but a new scientific decision-making method combined with real option theory and game theory on its basis. In this paper, real option theory is incorporated with game theory on the basis of traditional investment decision making. In the assessment of R&D projects’option value with real option theory, the problems arising from non-reversible of costs, uncertainty, and flexibility are addressed. Moreover, by analyzing competitors’interactive with game theory, possible equilibrium formulates and conditions for these equilibriums are obtained and option game model of R&D investment decision-making is constructed, thereby determining optimized investment opportunities and strategies.
This paper reviews and evaluates basic theories of R&D investment decision-making. Traditional means of R&D investment decision-making are analyzed with discussion of their limits. The advantages of real option theory in dealing with uncertainty in R&D investment decision-making are discussed, and the option feature and game feature in R&D investment are anatomized. On that basis, an application framework of option game theory in R&D investment decision-making is built, and from both angles of the enterprise’s competitive status and the competitor’s strategy, R&D investment strategy-selecting mode and first-mover advantages and disadvantages are analyzed. The uncertainties, as well as their impact on project value, are identified, with mathematical description, so that R&D investment project value structure is further ascertained from the perspective of option games, to form a solid theoretical foundation for option game price fixing model.
With real option price fixing theory, dynamic planning and simulation, aiming at R&D investment timing and strategy, an option-game model of R&D investment decision-making under the condition of market uncertainty and technical uncertainty is constructed. Under the uncertainty of market, considering the randomness of unexpected events and various kinds of enterprises involved in the R&D competition, on the assumption that random market demand is in line with the geometric Brownian motion and the original investment costs are different, an asymmetric, duopoly-monopoly, and continuous game-option model is established to gain the value functions and investment thresholds of corporations as followers, leaders, and investors, respectively. The impact on investment threshold imposed by unexpected events and investment cost is analyzed, and the occurrence forms and conditions of the three equilibrium strategies are discussed. The analysis shows that the investment threshold of followers is highly sensitive to the variation of operation cost, whereas that of leaders is highly sensitive to original investment cost; though instantaneous fluctuation rates and unexpected events result in the rise of investment threshold, they impose a larger impact on those of followers; the optimized R&D investment strategy relied on cost differences and initiatives of distinguished enterprises.
According to Weeds’model concerning technical uncertainty, the option-game model on condition of technical uncertainty is constructed on the assumption that enterprises’R&D capabilities are asymmetric, as well as their investment costs, achieving the value functions and investment thresholds of corporations, as followers, leaders, and investors, respectively. The following analysis focuses on the impact of enterprises’own R&D capacity and competitors’capability on the value of investment threshold. And the result demonstrates that the rise of own capability contributes to drop of threshold, while the rise of competitors gives rise to increase of threshold. Both of them play a large impact on threshold of followers. The analysis of investment strategies related to asymmetric duopoly-monopoly enterprises gives rise to an equilibrium result different from that gained in traditional research, indicating possible existence of sequential equilibrium investment. This possibility is further verified by means of numerical explanation and simulation.
对R&D投资决策的基本理论进行回顾和评述。分析传统R&D投资决策方法及其局限性,论述实物期权理论处理R&D投资过程中不确定性的优势,剖析R&D投资的期权特性和博弈特性。在此基础上,建立期权博弈理论在R&D投资决策中的应用框架,从企业的竞争地位和竞争者的战略反应两个角度,分析R&D投资策略选择模式以及R&D投资中的先动优势和劣势,识别R&D投资的不确定性及其对项目价值的影响,对不确定性进行数学描述,进一步从期权博弈的角度明确R&D投资项目价值构成,为构建期权博弈定价模型奠定理论基础。
运用实物期权定价、动态规划和仿真方法,针对R&D投资时机和策略选择,构造市场不确定条件下和技术不确定条件下的R&D投资决策的期权博弈模型。在市场不确定条件下,考虑突发事件具有随机性以及参与R&D竞争的企业的不同质性,假定随机市场需求符合带跳的几何布朗运动,R&D初始投资成本和经营成本均不相同,构建不对称的双寡头垄断的连续期权博弈模型,得到跟随者、领先者、同时投资者的价值函数和投资临界点,分析突发事件和投资成本对投资临界点的影响,讨论三种均衡策略的发生形式和条件。分析表明:跟随者投资临界值对经营成本的变化更敏感,而领先者投资临界值对初始投资成本的变动更敏感;瞬时波动率和突发事件都能导致投资临界值的增加,但是对跟随者投资临界值的影响更显著;企业最优投资均衡策略取决于竞争双方的成本差异和先动优势。
在Weeds的技术不确定模型基础上,假设企业间R&D能力和投入成本均不对称,构建技术不确定条件下的期权博弈模型,得到跟随者、领先者和同时投资者的价值函数和投资临界值,重点分析企业自身R&D能力及竞争者的R&D能力对投资临界值的影响。结果表明:企业自身R&D能力的增强可以降低投资临界值,竞争对手R&D能力的增强将提高投资临界值,而且都是对跟随者投资临界值的影响更显著。对不对称双寡头垄断企业的投资策略进行分析,得到不同于前人的均衡结果,指出仍然可能存在序贯均衡,用数值释例和仿真方法验证序贯均衡的存在。
For an enterprise, research and development (R&D) is the basis of its core competence, and also an important component of its long-term development strategy. In the quantitative assessment of R&D projects, conventional means of investment decision making, generally based on net present value, neglects some significant factors, including the uncertainty of investment projects, the allowable delay of vestment time, the non-reversible of costs, and competitive. Such problems result in hard-mode strategy of investment, which always is“now or never”. This will give rise to lose of investment opportunities as well as room to grow. Thus, it is evident that scientific identification of investment time plays a key role in R&D activities on the condition of uncertain competitive environment. Option game theory is not a complete negation of conventional investment decision-making method, but a new scientific decision-making method combined with real option theory and game theory on its basis. In this paper, real option theory is incorporated with game theory on the basis of traditional investment decision making. In the assessment of R&D projects’option value with real option theory, the problems arising from non-reversible of costs, uncertainty, and flexibility are addressed. Moreover, by analyzing competitors’interactive with game theory, possible equilibrium formulates and conditions for these equilibriums are obtained and option game model of R&D investment decision-making is constructed, thereby determining optimized investment opportunities and strategies.
This paper reviews and evaluates basic theories of R&D investment decision-making. Traditional means of R&D investment decision-making are analyzed with discussion of their limits. The advantages of real option theory in dealing with uncertainty in R&D investment decision-making are discussed, and the option feature and game feature in R&D investment are anatomized. On that basis, an application framework of option game theory in R&D investment decision-making is built, and from both angles of the enterprise’s competitive status and the competitor’s strategy, R&D investment strategy-selecting mode and first-mover advantages and disadvantages are analyzed. The uncertainties, as well as their impact on project value, are identified, with mathematical description, so that R&D investment project value structure is further ascertained from the perspective of option games, to form a solid theoretical foundation for option game price fixing model.
With real option price fixing theory, dynamic planning and simulation, aiming at R&D investment timing and strategy, an option-game model of R&D investment decision-making under the condition of market uncertainty and technical uncertainty is constructed. Under the uncertainty of market, considering the randomness of unexpected events and various kinds of enterprises involved in the R&D competition, on the assumption that random market demand is in line with the geometric Brownian motion and the original investment costs are different, an asymmetric, duopoly-monopoly, and continuous game-option model is established to gain the value functions and investment thresholds of corporations as followers, leaders, and investors, respectively. The impact on investment threshold imposed by unexpected events and investment cost is analyzed, and the occurrence forms and conditions of the three equilibrium strategies are discussed. The analysis shows that the investment threshold of followers is highly sensitive to the variation of operation cost, whereas that of leaders is highly sensitive to original investment cost; though instantaneous fluctuation rates and unexpected events result in the rise of investment threshold, they impose a larger impact on those of followers; the optimized R&D investment strategy relied on cost differences and initiatives of distinguished enterprises.
According to Weeds’model concerning technical uncertainty, the option-game model on condition of technical uncertainty is constructed on the assumption that enterprises’R&D capabilities are asymmetric, as well as their investment costs, achieving the value functions and investment thresholds of corporations, as followers, leaders, and investors, respectively. The following analysis focuses on the impact of enterprises’own R&D capacity and competitors’capability on the value of investment threshold. And the result demonstrates that the rise of own capability contributes to drop of threshold, while the rise of competitors gives rise to increase of threshold. Both of them play a large impact on threshold of followers. The analysis of investment strategies related to asymmetric duopoly-monopoly enterprises gives rise to an equilibrium result different from that gained in traditional research, indicating possible existence of sequential equilibrium investment. This possibility is further verified by means of numerical explanation and simulation.
引文
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69余冬平,邱菀华. R&D研发投资决策的不对称双头垄断期权博弈模型.系统工程. 2005, 23(2): 31-34
70薛明皋,龚朴.非对称情形下R&D竞争项目的策略性投资.数学物理学报. 2008, 28(5): 794-801
71蔡强.基于期权博弈的专利投资决策研究.电子科技大学博士学位论文. 2009: 75-92
72 W. C. Kester. Today's Option for Tomorrow's Growth. Harvard Business Review. 1984, (March-April): 153-160
73 K. J. M. Huisman, P. M. Kort and G. Pawlina. Strategic Investment under Uncertainty: Merging Real Options with Game Theory. Working Paper of Tiburg University. http://ideas.repec.org/p/dgr/kubcen/20036.html
74 K. J. M. Huisman, P. M. Kort. Strategic Technology Investment under Uncertainty. Center Discussion Paper of Tilburg University. http://ideas.repec. org/p/dgr/kubcen/199918.html
75 J. J. Thijssen, K. J. Huisman. The Effect of Information Streams on Capital Budgeting Decisions. European Journal of Operational Research. 2004, 157(3): 15-35
76 R. J. Kanffman, X. T. Li. Technoloty Competition and Optimal Investment Timing: A Real Options Perspective. Working Paper of Minnesota University. 2004: 42-85
77 H. Weeds. Reverse Hysteresis: R&D Investment with Stochastic Innovation. Working Paper of Cambridge University. hhtp://www2.warwick.ac.uk/fa/soc/ economics/research/papers/twerp578.pdf
78 H. C. Hoppe. A Strategic Search Model of Technology Adoption and Policy. Advances in Applied Microeconomics. 2000, (9): 197-214
79吴建祖,宣慧玉.经营成本对企业研发投资决策影响的期权博弈分析.系统工程. 2004, 22(5): 30-34
80夏晖,曾勇.不完全竞争环境下不对称企业技术创新战略投资.管理科学学报. 2005, 8(1): 30-41
81何德忠,孟卫东.企业投资决策的期权博弈分析.重庆大学学报. 2004, 27(10): 164-166
82黄学军,吴冲锋.不确定环境下研发投资决策的期权博弈模型.中国管理科学. 2006, 14(5): 33-37
83宋成华.日本研发投资效率分析.黑龙江大学出版社, 2009: 55-60
84杨勇,达庆利.企业产品升级投资决策研究.中国管理科学. 2005, 13(1): 65-70
85 K. J. Arrow, A. C. Fisher. Environmental Preservation, Uncertainty and Irreversibility. Quarterly Journal of Economics. 1974, 88(3): 198-312
86邓光军.实物期权及其在IT投资中的应用评价.预测. 2004, (2): 35-40
87 Boyle. A Lattice Framework for Option Pricing with Two State variables. Journal of Financial and Quantitative Analysis. 1988, (23): 1-23
88 Y. Tian. A Modified Lattice Approach to Option Pricing. Journal of Future Markets. 1993, (13): 563-577
89 R. Merton. Theory of Rational Option Pricing. Bell Journal of Economics and Management Science. 1973, 4(2): 141-183
90邵天习,张刚刚.期权博弈理论在投资决策中的应用研究.武汉理工大学学报. 2007, 29(6): 151-153
91 H. T. Smit, L. Trigeorgis. Strategic Investment: Real Options and Games. Princeton University Press, 2004: 50-154
92 J. S. Park. Opportunity Recognition and Product Innovation in Entrepreneurial Hi-tech Start-us a New Perspective and Supporting Case Study. Thechnovation. 2005, (5): 739-752
93 R. Kristan, Miltersen. R&D Investment with Competitive Interactions. Review of Finance. 2004,(8): 355-401
94田野.多阶段投资决策的复合期权模型及应用.哈尔滨工业大学硕士学位论文. 2007: 15-45
95何志伟.复合期权与路径相关期权定价理论模型、数值模拟及应用研究.华中科在大学博士学位论文. 2006: 27-60
96 D. Fudenberg, J. Tirole. The Fat–Cat Effect,The Puppy–Dog Ploy, and The Lean and Hungry Look. American Economic Review. 1984, (3): 361-366
97仲伟俊,梅姝娥.企业技术创新管理理论与方法.科学出版社, 2009: 11-48
98张春玲.传统的先动优势和后动优势理论的缺失分析.生产力研究. 2008, (1): 24-27
99师萍,张蔚虹.中国R&D投入的绩效分析与制度支持研究.科学出版社, 2008: 86-143
100陈劲,伍蓓.研发项目管理.机械工业出版社, 2009: 31-98
101 A. J. Salter. The Economic Benefits of Publicly Funded Basic Research: Acrtical Review. Research Policy. 2001, (30): 50-59
102 K. Arrow. The Economics Implications of Learning by Doing. Review of Economics Studies. 1962: 69-82
103 J. Stiglitz, A. Weiss. Credit Rationing in Markets with Imperfect Information. American Economic Review. 1981, (71): 35-53
104 R. Stenbacka, M. M. Tombak. Technology Polcy and The Organization of R&D. Economic Behavior Organization. 1998, 36(4): 32-54
105 G. G?tz. Strategic Timing of Adoption of New Technology under Uncertainty: A Note. Review of Economic Studies. 2002, 69(3): 11-34
106 A. K. Dixit, R. S. Pindck. Investment in Technological Innovations: An Option Pricing Approach. Journal of Financial Economics. 1997, 44(3): 37-46
107余冬平,邱菀华.双寡头战略期权执行博弈均衡投资决策研究.北京航空航天大学学报. 2006, 19(4): 5-8
108余冬平.基于二重随机因素的对称双头垄断期权博弈模型.中国管理科学. 2007, 15(5): 113-118
109余冬平,邱菀华. R&D战略投资决策的期权博弈分析. 2006中国控制与决策学术年会论文集. 2006: 1093-1098
110 M. A. Dias, J. P. Teixeira. Continuous-Time Option Game: Review of Models and Extensions Part 1: Duopoly under Uncertainty. 7th Annual International Real Options Coference, Washington DC, 2003, http://www.realop tions.org /papers2003/Dias Teixeira Option-games.pdf
111余冬平.基于竞争互动的实物期权均衡执行战略研究.系统工程理论与实践. 2007, (5): 12-21
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42 F. Smets. Exporting Versus FDI: The Effect of Uncertainty, Irreversibility and Strategic Interactions. Working Paper of Yale University. 1991: 4-35
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44 B. Lambrecht, W. Perraudin. Options Game. Working Paper of Cambridge University. 1994: 143-178
45 K. J. M. Huisman, P. M. Kort. Effects of Strategic Interactions on The Option Value of Waiting. Working Paper of Tilburg University, 1999: 42-57
46 K. J. M. Huisman, P. M. Kort. Strategic Technology Adoption Taking into Future Technology Improvements: A Real Option Approach. European Journal of Operational Research. 2004, 159(3): 705-728
47 K. J. M. Huisman. Technology Investment: A Game Real Options Approach. Kluwer Academic Publishers, 2001: 54-86
48 S. R. Grenadier. Game Choices: The Intersection of Real Options and Game Theory. Risk Books. 2000: 35-89
49何德忠,孟卫东.期权博弈理论发展综述.生产力研究. 2007, (2): 148-150
50段静静.国内外期权博弈研究综述.发展研究. 2009, (9): 62-64
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57扈文秀,韩仁德.期权博弈的分类及其在不完全信息下的均衡策略研究.科技进步与对策. 2006, (7): 105-109
58洪开荣.期权博弈评价理论.武汉大学出版社, 2007: 10-12
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64杨勇,达庆利. R&D投资评价的期权博弈方法应用研究.东南大学学报(社会科学版). 2005, 7(4): 51-54
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66王滨.不确定条件下投资的博弈分析.华中科技大学博士学位论文. 2005: 44-89
67夏轶群,陈俊芳.技术不确定的研发项目投资时机期权博弈分析.科研管理.2009, 30(2): 126-129
68雷星晖,李来俊.竞争环境下基于期权博弈的R&D投资决策研究.管理科学. 2004, 17(1): 85-89
69余冬平,邱菀华. R&D研发投资决策的不对称双头垄断期权博弈模型.系统工程. 2005, 23(2): 31-34
70薛明皋,龚朴.非对称情形下R&D竞争项目的策略性投资.数学物理学报. 2008, 28(5): 794-801
71蔡强.基于期权博弈的专利投资决策研究.电子科技大学博士学位论文. 2009: 75-92
72 W. C. Kester. Today's Option for Tomorrow's Growth. Harvard Business Review. 1984, (March-April): 153-160
73 K. J. M. Huisman, P. M. Kort and G. Pawlina. Strategic Investment under Uncertainty: Merging Real Options with Game Theory. Working Paper of Tiburg University. http://ideas.repec.org/p/dgr/kubcen/20036.html
74 K. J. M. Huisman, P. M. Kort. Strategic Technology Investment under Uncertainty. Center Discussion Paper of Tilburg University. http://ideas.repec. org/p/dgr/kubcen/199918.html
75 J. J. Thijssen, K. J. Huisman. The Effect of Information Streams on Capital Budgeting Decisions. European Journal of Operational Research. 2004, 157(3): 15-35
76 R. J. Kanffman, X. T. Li. Technoloty Competition and Optimal Investment Timing: A Real Options Perspective. Working Paper of Minnesota University. 2004: 42-85
77 H. Weeds. Reverse Hysteresis: R&D Investment with Stochastic Innovation. Working Paper of Cambridge University. hhtp://www2.warwick.ac.uk/fa/soc/ economics/research/papers/twerp578.pdf
78 H. C. Hoppe. A Strategic Search Model of Technology Adoption and Policy. Advances in Applied Microeconomics. 2000, (9): 197-214
79吴建祖,宣慧玉.经营成本对企业研发投资决策影响的期权博弈分析.系统工程. 2004, 22(5): 30-34
80夏晖,曾勇.不完全竞争环境下不对称企业技术创新战略投资.管理科学学报. 2005, 8(1): 30-41
81何德忠,孟卫东.企业投资决策的期权博弈分析.重庆大学学报. 2004, 27(10): 164-166
82黄学军,吴冲锋.不确定环境下研发投资决策的期权博弈模型.中国管理科学. 2006, 14(5): 33-37
83宋成华.日本研发投资效率分析.黑龙江大学出版社, 2009: 55-60
84杨勇,达庆利.企业产品升级投资决策研究.中国管理科学. 2005, 13(1): 65-70
85 K. J. Arrow, A. C. Fisher. Environmental Preservation, Uncertainty and Irreversibility. Quarterly Journal of Economics. 1974, 88(3): 198-312
86邓光军.实物期权及其在IT投资中的应用评价.预测. 2004, (2): 35-40
87 Boyle. A Lattice Framework for Option Pricing with Two State variables. Journal of Financial and Quantitative Analysis. 1988, (23): 1-23
88 Y. Tian. A Modified Lattice Approach to Option Pricing. Journal of Future Markets. 1993, (13): 563-577
89 R. Merton. Theory of Rational Option Pricing. Bell Journal of Economics and Management Science. 1973, 4(2): 141-183
90邵天习,张刚刚.期权博弈理论在投资决策中的应用研究.武汉理工大学学报. 2007, 29(6): 151-153
91 H. T. Smit, L. Trigeorgis. Strategic Investment: Real Options and Games. Princeton University Press, 2004: 50-154
92 J. S. Park. Opportunity Recognition and Product Innovation in Entrepreneurial Hi-tech Start-us a New Perspective and Supporting Case Study. Thechnovation. 2005, (5): 739-752
93 R. Kristan, Miltersen. R&D Investment with Competitive Interactions. Review of Finance. 2004,(8): 355-401
94田野.多阶段投资决策的复合期权模型及应用.哈尔滨工业大学硕士学位论文. 2007: 15-45
95何志伟.复合期权与路径相关期权定价理论模型、数值模拟及应用研究.华中科在大学博士学位论文. 2006: 27-60
96 D. Fudenberg, J. Tirole. The Fat–Cat Effect,The Puppy–Dog Ploy, and The Lean and Hungry Look. American Economic Review. 1984, (3): 361-366
97仲伟俊,梅姝娥.企业技术创新管理理论与方法.科学出版社, 2009: 11-48
98张春玲.传统的先动优势和后动优势理论的缺失分析.生产力研究. 2008, (1): 24-27
99师萍,张蔚虹.中国R&D投入的绩效分析与制度支持研究.科学出版社, 2008: 86-143
100陈劲,伍蓓.研发项目管理.机械工业出版社, 2009: 31-98
101 A. J. Salter. The Economic Benefits of Publicly Funded Basic Research: Acrtical Review. Research Policy. 2001, (30): 50-59
102 K. Arrow. The Economics Implications of Learning by Doing. Review of Economics Studies. 1962: 69-82
103 J. Stiglitz, A. Weiss. Credit Rationing in Markets with Imperfect Information. American Economic Review. 1981, (71): 35-53
104 R. Stenbacka, M. M. Tombak. Technology Polcy and The Organization of R&D. Economic Behavior Organization. 1998, 36(4): 32-54
105 G. G?tz. Strategic Timing of Adoption of New Technology under Uncertainty: A Note. Review of Economic Studies. 2002, 69(3): 11-34
106 A. K. Dixit, R. S. Pindck. Investment in Technological Innovations: An Option Pricing Approach. Journal of Financial Economics. 1997, 44(3): 37-46
107余冬平,邱菀华.双寡头战略期权执行博弈均衡投资决策研究.北京航空航天大学学报. 2006, 19(4): 5-8
108余冬平.基于二重随机因素的对称双头垄断期权博弈模型.中国管理科学. 2007, 15(5): 113-118
109余冬平,邱菀华. R&D战略投资决策的期权博弈分析. 2006中国控制与决策学术年会论文集. 2006: 1093-1098
110 M. A. Dias, J. P. Teixeira. Continuous-Time Option Game: Review of Models and Extensions Part 1: Duopoly under Uncertainty. 7th Annual International Real Options Coference, Washington DC, 2003, http://www.realop tions.org /papers2003/Dias Teixeira Option-games.pdf
111余冬平.基于竞争互动的实物期权均衡执行战略研究.系统工程理论与实践. 2007, (5): 12-21
112 H. Weeds. Strategy Delay in A Real Option Model of R&D Competition. Working Paper of Cambridge University. 1999: 50-89