风险投资中的博弈论模型
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摘要
自上世纪初博弈论形成以来,它在经济学方面的应用就越来越广泛,并有大量成熟的理论和模型出现。在近20年,随着新经济和信息技术的迅速发展,风险投资开始盛行起来。最初,只是一些个人投资者进入这一高风险、高收益的投资领域,参与个人创业者的项目;现在,则更多是专业的投资机构雇佣专业的投资分析师进行风险投资项目的分析和投资运作。对于风险投资的研究,目前的成果主要侧重于从风险投资者的角度对投资项目和创业者进行评价,而忽略了双方之间存在的博弈行为。
本文从风险投资者和创业者双方的博弈行为和策略出发,将博弈论用于风险投资运作的研究和分析,主要工作如下:
在非连续努力水平的情况下,建立风险投资者和创业者之间的基础博弈模型,在此基础上,对第三阶段的博弈进行着重分析,并依照风险投资者和创业者决策变量的不同,以及双方是否进行合作博弈,分别建立了四个不同的博弈模型。
建立了风险投资者和创业者分别以投资额度和努力水平为决策变量的非合作博弈模型,证明了该博弈模型Nash均衡解的存在性,分析了创业者的努力水平和风险投资者投资额度之间的互动性,并由此给出了求该博弈模型Nash均衡解的迭代算法。
建立了风险投资者和创业者分别以股权分配比例和努力水平为决策变量的非合作博弈模型,同样证明了其Nash均衡的存在性,并分析了股权分配比例对努力水平的影响,给出了一个求得满意解的方法。
建立了风险投资者和创业者分别以投资额度和努力水平为决策变量的合作博弈模型,给出了合作联盟最优解的必要条件,分析了合作模型的联盟最优解和非合作博弈模型的Nash均衡解之间的关系、联盟最优解的稳定性,以及保持联盟最优解稳定所需的附加条件,并给出了达到联盟最优解的迭代算法。
建立了风险投资者和创业者分别以股权分配比例和努力水平为决策变量的合作博弈模型,给出了联盟最优解的必要条件,分析了合作模型的联盟最优解和非合作模型的满意解之间的关系、联盟最优解的稳定性,以及联盟达到最大效用的分配原则。
Game Theory has had a more and more extensive application in economic fields since its foundation in last century. And a large number of integrated theories and models have been arisen. In the latest decade, venture capital has been prevailing as the rapid development of new economies and information technologies. At first, only some individual investors entered into this high risk and profitable investment taking part in the project of individual entrepreneurs. And now, the venture capital projects have been analyzed and operated by occupational investment analysts in the professional investing organizations. However, the present studies focus on the evaluation of investing projects and entrepreneurs from the venture capitalists' aspect ignoring the game behaviors between them.
In this dissertation, game theory is used to study and analyze the operation of venture capital from the aspect of game behaviors and strategies of venture capitalists and entrepreneurs. The main works are as follows:
Under the condition of in-continuous hard-working level, it establishes that the basic game model between the venture capitalists and entrepreneurs. Based on this model, the third stage of games stress is analyzed. And four game theory models are established according to different decision variables of venture capital and the concrete game structure, non-cooperative or cooperative.
A non-cooperative game model is presented with the amount of investment and hard-working level as venture capitalists' and entrepreneurs' strategies variables. The Nash equilibrium of this model is proven existent. And it is argued that there is interaction between the level of entrepreneurs' hardworking and the amount of venture capitals. Moreover, the iterative algorithm is derived accordingly for solving the Nash equilibrium of this model.
A non-cooperative game model is presented with the ratio of shares distribution and hard-working level as venture capitalists' and entrepreneurs' strategies variables. The existence of Nash equilibrium is proven in the same way. It is also proven that the ratio of shares distribution affects hard-working level. And the means to find the satisfactory solution are given.
A cooperative game model is established with the amount of investment and hard-working level as venture capitalists' and entrepreneurs' strategies variables. The necessary conditions of coalition optimal solution are presented. And it is analyzed the interaction between the coalition optimal solution of cooperative game model and the Nash equilibrium solution of non-cooperative game model and the stability of coalition optimal and the adjunctive conditions for keeping coalition optimal stable. The iterative algorithm is derived to reach the coalition optimal solution.
A cooperative game model is established with the ratio of shares distribution and hard-working level as venture capitalists' and entrepreneurs' strategies variables. The necessary conditions of coalition optimal solution are presented. And it is analyzed the interaction between the coalition optimal solution of cooperative game model and the satisfactory solution of non-cooperative game model, the stability of coalition optimal and the adjunctive conditions for keeping coalition optimal stable and the distribution principle of maximal coalition utility.
本文从风险投资者和创业者双方的博弈行为和策略出发,将博弈论用于风险投资运作的研究和分析,主要工作如下:
在非连续努力水平的情况下,建立风险投资者和创业者之间的基础博弈模型,在此基础上,对第三阶段的博弈进行着重分析,并依照风险投资者和创业者决策变量的不同,以及双方是否进行合作博弈,分别建立了四个不同的博弈模型。
建立了风险投资者和创业者分别以投资额度和努力水平为决策变量的非合作博弈模型,证明了该博弈模型Nash均衡解的存在性,分析了创业者的努力水平和风险投资者投资额度之间的互动性,并由此给出了求该博弈模型Nash均衡解的迭代算法。
建立了风险投资者和创业者分别以股权分配比例和努力水平为决策变量的非合作博弈模型,同样证明了其Nash均衡的存在性,并分析了股权分配比例对努力水平的影响,给出了一个求得满意解的方法。
建立了风险投资者和创业者分别以投资额度和努力水平为决策变量的合作博弈模型,给出了合作联盟最优解的必要条件,分析了合作模型的联盟最优解和非合作博弈模型的Nash均衡解之间的关系、联盟最优解的稳定性,以及保持联盟最优解稳定所需的附加条件,并给出了达到联盟最优解的迭代算法。
建立了风险投资者和创业者分别以股权分配比例和努力水平为决策变量的合作博弈模型,给出了联盟最优解的必要条件,分析了合作模型的联盟最优解和非合作模型的满意解之间的关系、联盟最优解的稳定性,以及联盟达到最大效用的分配原则。
Game Theory has had a more and more extensive application in economic fields since its foundation in last century. And a large number of integrated theories and models have been arisen. In the latest decade, venture capital has been prevailing as the rapid development of new economies and information technologies. At first, only some individual investors entered into this high risk and profitable investment taking part in the project of individual entrepreneurs. And now, the venture capital projects have been analyzed and operated by occupational investment analysts in the professional investing organizations. However, the present studies focus on the evaluation of investing projects and entrepreneurs from the venture capitalists' aspect ignoring the game behaviors between them.
In this dissertation, game theory is used to study and analyze the operation of venture capital from the aspect of game behaviors and strategies of venture capitalists and entrepreneurs. The main works are as follows:
Under the condition of in-continuous hard-working level, it establishes that the basic game model between the venture capitalists and entrepreneurs. Based on this model, the third stage of games stress is analyzed. And four game theory models are established according to different decision variables of venture capital and the concrete game structure, non-cooperative or cooperative.
A non-cooperative game model is presented with the amount of investment and hard-working level as venture capitalists' and entrepreneurs' strategies variables. The Nash equilibrium of this model is proven existent. And it is argued that there is interaction between the level of entrepreneurs' hardworking and the amount of venture capitals. Moreover, the iterative algorithm is derived accordingly for solving the Nash equilibrium of this model.
A non-cooperative game model is presented with the ratio of shares distribution and hard-working level as venture capitalists' and entrepreneurs' strategies variables. The existence of Nash equilibrium is proven in the same way. It is also proven that the ratio of shares distribution affects hard-working level. And the means to find the satisfactory solution are given.
A cooperative game model is established with the amount of investment and hard-working level as venture capitalists' and entrepreneurs' strategies variables. The necessary conditions of coalition optimal solution are presented. And it is analyzed the interaction between the coalition optimal solution of cooperative game model and the Nash equilibrium solution of non-cooperative game model and the stability of coalition optimal and the adjunctive conditions for keeping coalition optimal stable. The iterative algorithm is derived to reach the coalition optimal solution.
A cooperative game model is established with the ratio of shares distribution and hard-working level as venture capitalists' and entrepreneurs' strategies variables. The necessary conditions of coalition optimal solution are presented. And it is analyzed the interaction between the coalition optimal solution of cooperative game model and the satisfactory solution of non-cooperative game model, the stability of coalition optimal and the adjunctive conditions for keeping coalition optimal stable and the distribution principle of maximal coalition utility.
引文
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