外国经济与管理  2018, Vol. 40 Issue (3): 79-91     
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外国经济与管理
2018年40卷第3期
刘志迎, 周章庆, 陈明春, 廖素琴
Liu Zhiying, Zhou Zhangqing, Chen Mingchun, Liao Suqin
商业模式需要创新还是模仿?——基于实物期权博弈的策略研究
Business model innovation or imitation? strategy study based on real option game theory
外国经济与管理, 2018, 40(3): 79-91
Foreign Economics & Management, 2018, 40(3): 79-91.

文章历史

收稿日期: 2017-05-11
《外国经济与管理》
2018第40卷第3期
商业模式需要创新还是模仿?——基于实物期权博弈的策略研究
刘志迎, 周章庆, 陈明春, 廖素琴     
中国科学技术大学 管理学院,安徽 合肥 230026
摘要:企业生命周期中商业模式是不断变动的,本文借用实物期权博弈模型,解决不确定条件下商业模式创新或模仿策略选择问题。由于商业模式创新很难实现专利保护,模仿将难以避免。两期二叉树博弈分析结果表明:商业模式创新和模仿的价值只和企业市场份额α和基期基准倍数I(基期基准现金流与商业模式创新投入比值,表示项目初期的收益率)有关,当基期基准倍数很高且企业份额相差不大时,两个企业都进行商业模式创新是最优选择;当基期基准倍数中等且企业份额相差不大时,有可能出现小企业商业模式创新,大企业模仿的均衡策略组合;当基期基准倍数不低且企业份额相差较大时,则会出现大企业创新,小企业模仿的“智猪博弈”;当基期基准倍数较小时,大、小企业都不会有进行商业模式创新的动机。所以,理论上回答了商业模式创新或模仿的理性选择依据,指出商业模式创新与否要根据企业所处的市场竞争格局和项目初期收益率进行综合考量;拓展了实物期权博弈模型在商业模式创新价值评估中的应用,对企业从事商业模式创新具有重要现实指导意义。
关键词创新商业模式创新模仿实物期权博弈
Business Model Innovation or Imitation? Strategy Study Based on Real Option Game Theory
Liu Zhiying, Zhou Zhangqing, Chen Mingchun, Liao Suqin     
School of Management, University of Science and Technology of China, Hefei 230026, China
Summary: The business model is constantly changing in the enterprise life cycle. A large number of studies show that business model innovation enables enterprises to improve their processes and operation modes, reduce costs, create new markets, improve market efficiency, gain competitive advantages, and achieve higher value and business performance. However, since returns on business model innovation are uncertain and business model innovation can easily be imitated by competitors, it is more difficult to evaluate the value of business model innovation. This paper solves the problem of business model innovation or imitation strategy choice under uncertain conditions by constructing a real option game model. The model is based on the assumption of a duopoly market, namely when enterprise A carries out business model innovation, enterprise B can choose to innovate alone or imitate in the middle period. The results of two-stage binary tree analysis show that the value of business model innovation or imitation is only related to enterprise market share α and base period multiple I(a ratio of base period cash flow to innovation investment). When the base period multiple is very high and the enterprise shares are not much different, business model innovation is the best choice for both the two companies. When the base period multiple is medium and the enterprise shares are not much different, it is possible that there is a combination of equilibrium strategies that the small enterprise participates in business model innovation and the large enterprise business model imitation. When the base period multiple is not low and the enterprise shares are much different, there is a ‘pig game’ that large enterprise participates in business model innovation, and the small enterprise business model imitation; when the base period multiple is low, both small and large enterprises do not have the motivation for innovation. Therefore, business model innovation or imitation needs to take current market shares and initial returns of a project into account. This paper expands the application of real option, which is of great significance to the construction of business model innovation value evaluation model. In the field of business model innovation, theoretical concept construction, measurement scale development and empirical research have been basically completed, which focus on the impact of business model innovation on business performance. Few studies have analyzed the value of business model innovation from the perspectives of mathematical models and game theory, so it is a relatively new perspective to evaluate the value of innovation and imitation by using the real option game theory. Business model innovation is a systematic change, which is more complex than common project investment. This paper highlights consideration of uncertainty and opponent decision-making, which is more in line with the actual situation. On the other hand, the existing research on real option mostly adopts Black-Scholes option pricing method. However, the returns on business model innovation are sustained, belonging to American-style option, so we adopt the binary tree pricing method to take the revenues during the project period into account, providing a directional basis for future research and development. In the existing literature, the NPV method is commonly used in enterprise investment analysis and business model profit forecasting. The real option game has not been widely used, and more researchers are required to enrich the method for more rational use in practice. Firstly, the problem becomes more complex and closer to reality when considering multiple actors and multiple policy choices. When the binary option is exceeded, the binary tree method will not be applicable. Secondly, another complicated task is about the measurement of uncertainty in real option. There are many factors that have risks. It is a future research direction for scholars to unify them into one variable or independent comprehensive analysis of multiple variables.
Key words: innovation; business model innovation; imitation; real option; game theory

一、引 言

近年来互联网的兴起(Amit和Zott,2001)和新兴市场的发展(Prahalad和Hart,2002;Seelos和Mair,2007;Thompson和MacMillan,2010)促使商业模式及其创新成为当下学术研究的热点。“大众创新,万众创业”是中国政府鼓励进行商业模式创新重大管理实践的政策号召。以往的研究表明,商业模式创新能使企业改善流程和运营方式,降低成本(Amit和Zott,2001),创造新的市场(Giesen等,2007),提高市场效率并获取竞争优势(Mitchell和Coles,2003),获得更高的价值和企业绩效(Schimmer等,2014),进而成为企业利润增长的新引擎(Pohle和Chapman,2006)。然而商业模式创新需要投入一定的资源,并伴随着收益不确定性的风险,企业管理者往往难以获得创新的成本和收益的准确数据,用传统现金流折现的方法评估项目投资价值有严重的局限性;同时由于商业模式自身特性较易被竞争者模仿(Teece,2010),这就导致不同规模的企业陷入决策困境:到底企业在改变商业模式时是应该优先选择创新还是等待模仿其他企业的创新成果?

以往研究中常常借助“智猪博弈”模型分析类似情景,认为小企业不要率先行动,跟随大企业的策略是最优选择(章成友,2011);另外一部分学者认为企业应该倾向于选择风险较小的策略,避免设计新的商业模式(Pateli和Giaglis,2005)。这些研究都是基于特定情况下的结论,未能准确地解释现实情况,例如淘宝优先开发了“双十一购物狂欢模式”,京东选择跟进;又如京东开发了“京东物流自营快递”,淘宝跟进模仿推出了“菜鸟驿站”。模仿能够规避一些不确定性,降低商业模式变动的成本,但会丧失模仿跟进以前阶段的收益;而创新虽然需要付出较高的成本,但也能使企业优先获得前期的收益。

商业模式创新是一种战略决策(Zott等,2011),企业投入一定的资源,改变企业现有的模式,以期获得未来收益,这本质上是一种投资,具有投资收益不确定性、不可逆性等特点(Shackleton等,2004)。Trigeorgis和Reuer(2017)认为实物期权是企业战略管理研究的重要手段,例如市场进入时机选择、并购、企业间竞争合作关系等。与股票中看涨期权类似,商业模式创新本质上是对未来现金流的看涨预期,但与投资金融期权产品相比,商业模式创新具有以下几个特点:(1)商业模式创新带来的现金流是持续的,其价值是不同时刻现金流折现的累积;而金融期权却没有这一特点,其价值与执行时标的物的价格相关,期中多头无法获得收益。(2)由于市场规模有限,商业模式创新的价值还会受到模仿者进入的时间和所占市场份额影响。(3)商业模式创新一般易被模仿,模仿者将不需要付出创新成本。

因此需要开发新的分析模型才能更加契合商业模式决策的实际情况。采用实物期权方法评估项目价值能较好的弥补传统方法的不足(Smit和Trigeorgis,2012),故本文利用期权理论中二叉树定价方法对商业模式创新或模仿的价值进行评估,再借助博弈论的方法解决不确定条件下创新或模仿的策略选择问题。

二、文献综述

学者们普遍认为商业模式是由企业独立活动组成的活动系统,包含企业的价值链活动以及顾客、产品和服务活动(Teece,2010;Afuah,2003;Casadesus-Masanell和Ricart,2010;Hedman和Kalling,2003;Markides,2008;Seddon等,2004;Zott和Amit,2010)。商业模式创新是对组织结构、运作模式、商业流程以及价值创造和传递等过程进行重新设计(Zott等,2011);Morris等(2005)指出企业需要不断调整商业模式来应对环境条件的变化,其中创新和模仿是两个商业模式调整的重要渠道。Gambardella和McGahan(2010)认为传奇企业通过商业模式创新形成企业结构,导致竞争者直接模仿或者在其基础进一步创新。商业模式创新的概念决定了商业模式可能无法像技术创新和产品创新一样获取保护专利,因而很容易被竞争对手模仿(Teece,2010)。章成友(2011)研究表明创新开拓者为模仿者节省了大量的创新成本开支,模仿追随者吸取了创新者的经验与教训,少走了弯路。另一方面,模仿者又会缺失延期跟进期间的净现金流(Smit和Ankum,1993)。总之过去学者过于强调商业模式创新带来的优势,而鲜有从经济模型角度探讨不确定性条件下商业模式变动时策略选择问题。

在实物期权领域,Dixit和Pindyck(1994)以及Kulatilaka等(1998)都认为企业投资决策可以看成与金融期权中的看涨期权,投资的价值和时机是由市场竞争交互影响的(Smit和Trigeorgis,2006)。Grenadier(2000)和Huisman(2013)为技术投资提供了可量化实物期权价值评估方法。Weeds(2002)针对两家竞争专利权的公司提出最佳投资策略,解释了为什么有些公司延迟专利权的开发投入,并认为当延迟投资存在价值并且投资价值会被竞争跟随者影响时,综合博弈论和实物期权理论是解决该类问题的重要工具,此后关于实物期权博弈理论才逐渐被丰富。Smit和Trigeorgis(2004)将实物期权和博弈论结合起来解决企业联盟间竞争合作决策问题。Lambrecht(2000)和Weeds等(2000)则考虑了不确定性条件下的创新延迟投入问题;在其基础上,Lambrecht(2004)利用实物期权模型解决企业并购的时机和策略问题,由于规模经济驱动,企业并购浪潮呈现周期性特征。Jan(2011)利用实物期权博弈模型分析了台湾两个双寡头连锁店在开辟新分店时的投资策略选择,提出完全信息下非合作博弈均衡,认为大型连锁企业比小型连锁企业有更多选择权,即当市场不增长时,大企业优先进入的情况下,小企业跟进将无法获得收益。近年来实物期权运用越来越广,Costantino等(2016)将实物期权用于评估柔性导向战略的价值,以期降低商品价格波动对供应链风险管理的影响。Smit和Trigeorgis(2017)依托实物期权原理开发了“战略NPV”法,这种将实物期权和博弈论结合起来的新价值评估方法为实物期权实践化运用做了有益的理论化探索。

商业模式创新属于投资的一种,但是它的特征使得其与前人构建的模型又不完全相同,本文借鉴期权的定价方法和博弈论竞争思想构建新的模型,探讨收益不确定条件下商业模式创新或模仿的选择问题,不仅深化商业模式创新的研究,同时相比于前人研究侧重理论构建,本文更加关注实物期权博弈的具体实践运用。

三、模型构建

(一)模型基础

预设市场有两个企业A和B,分别占有α和1–α的市场份额,例如用户数。将整个商业模式创新或模仿的寿命T(寿命期之外将不再具有价值)分为两期,创新者只能在t=0时进入,模仿者只能在t=T/2时进入。当两个企业同在新商业模式市场中竞争,原有市场份额会决定新市场的份额,这是由于平台型用户由于多年积累,用户转移成本过高,会被各自企业引导至新市场,份额比例不会发生太大变化,以“双十一购物狂欢节”为例,淘宝天猫创新出了这一新模式,京东也通过模仿跟进,根据《星图数据11.12:双十一大数据分析报告》显示,2016年天猫销售额占68.2%,京东为22.7%,可见与其市场份额3:1的比例非常接近。

假设创新投入C包括市场调研资金、模式设计成本、创新人员人力成本等,商业模式不具有专利,模仿者意味着不需要这些成本就能复制到创新者的商业模式,并瓜分一定的市场。

市场净现金流量指某一时刻现金流入与现金流出的差额,反应收益的大小。为了便于处理,认为企业只在t=T/2和t=T时两次收割现金流。设基期市场净现金流基准为S=ICI为基期基准倍数,I越大,商业模式创新初期收益越大,越有吸引力,此后净现金流在此基础上变化。由于不确定性的存在,t=T/2时净现金流S1有可能上升为uSu>1),也有可能下降为dSd<1),其中ud=1,ud的大小由市场不确定性决定,t=TS2同理;设无风险期利率为r,且上行概率 $p = \displaystyle\frac{{1 + r - d}}{{u - d}}$ ,下行概率 $1 - p = \displaystyle\frac{{u - 1 - r}}{{u - d}}$ ,变动情况如图1所示。如果同时创新进入,则A、B按现有份额分配市场净现金流;如果A创新,B在期中进入,则B进入前A独占S1,进入后按份额分配S2

(1)A、B都采取商业模式创新策略,则两期之后两企业项目价值分别为:

${V_{A2}} = \frac{{\alpha {S_1}}}{{1 + r}} + \frac{{\alpha {S_2}}}{{{{\left( {1 + r} \right)}^2}}} - C $ (1)
${V_{B2}} = \frac{{(1 - \alpha ){S_1}}}{{1 + r}} + \frac{{\left( {1 - \alpha } \right){S_2}}}{{{{\left( {1 + r} \right)}^2}}} - C $ (2)

(2)A进行商业模式创新,B在期中t=T/2时模仿跟进,则两期之后两企业该项目价值分别为:

${V_{A2}} = \frac{{{S_1}}}{{1 + r}} + \frac{{\alpha {S_2}}}{{{{\left( {1 + r} \right)}^2}}} - C $ (3)
${V_{B2}} = \frac{{\left( {1 - \alpha } \right){S_2}}}{{{{\left( {1 + r} \right)}^2}}} $ (4)

(3)B进行商业模式创新,A在期中t=T/2时模仿跟进,则两期之后两企业该项目价值分别为:

${V_{A2}} = \frac{{\alpha {S_2}}}{{{{\left( {1 + r} \right)}^2}}}$ (5)
${V_{B2}} = \frac{{{S_1}}}{{1 + r}} + \frac{{\left( {1 - \alpha } \right){S_2}}}{{{{\left( {1 + r} \right)}^2}}} - C$ (6)

(4)A、B都采取模仿策略,则市场无人进行商业模式创新,就没人能获得该市场的净现金流,则VA=0;VB=0。

图 1 市场净现金流S
图 2 博弈价值二叉树图

(二)模型计算

(1)A、B都采取商业模式创新策略,则

两期净现金流增长时,即uu

$V_{A2}^{uu} = \frac{{\alpha uS}}{{1 + r}} + \frac{{\alpha {u^2}S}}{{{{\left( {1 + r} \right)}^2}}} - C$ (7)
$V_{B2}^{uu} = \frac{{\left( {1 - \alpha } \right)uS}}{{1 + r}} + \frac{{\left( {1 - \alpha } \right){u^2}S}}{{{{\left( {1 + r} \right)}^2}}} - C$ (8)

第一期净现金流增长,第二期降低,即ud

$V_{A2}^{ud} = \frac{{\alpha uS}}{{1 + r}} + \frac{{\alpha S}}{{{{\left( {1 + r} \right)}^2}}} - C$ (9)
$V_{B2}^{ud} = \frac{{\left( {1 - \alpha } \right)uS}}{{1 + r}} + \frac{{\left( {1 - \alpha } \right)S}}{{{{\left( {1 + r} \right)}^2}}} - C$ (10)

第一期净现金流降低,第二期增长,即du

$V_{A2}^{du} = \frac{{\alpha dS}}{{1 + r}} + \frac{{\alpha S}}{{{{\left( {1 + r} \right)}^2}}} - C$ (11)
$V_{B2}^{du} = \frac{{\left( {1 - \alpha } \right)dS}}{{1 + r}} + \frac{{\left( {1 - \alpha } \right)S}}{{{{\left( {1 + r} \right)}^2}}} - C$ (12)

两期净现金流都降低,即dd

$V_{A2}^{dd} = \frac{{\alpha dS}}{{1 + r}} + \frac{{\alpha {d^2}S}}{{{{\left( {1 + r} \right)}^2}}} - C$ (13)
$V_{B2}^{dd} = \frac{{\left( {1 - \alpha } \right)dS}}{{1 + r}} + \frac{{\left( {1 - \alpha } \right){d^2}S}}{{{{\left( {1 + r} \right)}^2}}} - C$ (14)

根据上述t=T时情况, $V_{A2}^{uu}$ $V_{A2}^{ud}$ 可以推出t=T/2时,如图2所示,

$V_{A1}^u = V_{A2}^{uu} \times {\text{上行概率}} + V_{A2}^{ud} \times {\text{下行概率}} $ (15)
$\begin{aligned} V_{A1}^u = & \left( {\frac{{\alpha uS}}{{1 + r}} + \frac{{\alpha {u^2}S}}{{{{\left( {1 + r} \right)}^2}}} - C} \right) \times \frac{{1 + r - d}}{{u - d}} + \left( {\frac{{\alpha uS}}{{1 + r}} + \frac{{\alpha S}}{{{{\left( {1 + r} \right)}^2}}} - C} \right) \times \frac{{u - 1 - r}}{{u - d}} \\ {{ = }}& \alpha S\left[ {\frac{u}{{1 + r}} + \frac{{\left( {1 + r - d} \right){u^2} + \left( {u - 1 - r} \right)}}{{{{\left( {1 + r} \right)}^2}\left( {u - d} \right)}}} \right] - C\end{aligned}$ (16)

同理:

$\begin{aligned}V_{B1}^u &= \left[ {\frac{{\left( {1 - \alpha } \right)uS}}{{1 + r}} \!+\! \frac{{\left( {1 - \alpha } \right){u^2}S}}{{{{\left( {1 + r} \right)}^2}}} \!-\! C} \right] \!\times\! \frac{{1 + r - d}}{{u - d}} \!+\! \left[ {\frac{{\left( {1 - \alpha } \right)uS}}{{1 + r}} \!+\! \frac{{\left( {1 - \alpha } \right)S}}{{{{\left( {1 + r} \right)}^2}}} \!-\! C} \right] \!\times\! \frac{{u - 1 - r}}{{u - d}}\\ &{{ = }} \left( {1 - \alpha } \right)S\left[ {\frac{u}{{1 + r}} + \frac{{\left( {1 + r - d} \right){u^2} + \left( {u - 1 - r} \right)}}{{{{\left( {1 + r} \right)}^2}\left( {u - d} \right)}}} \right] - C\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad {(17)}\end{aligned}$
$V_{A1}^d = \alpha S\left[ {\frac{d}{{1 + r}} + \frac{{\left( {1 + r - d} \right) + \left( {u - 1 - r} \right){d^2}}}{{{{\left( {1 + r} \right)}^2}\left( {u - d} \right)}}} \right] - C$ (18)
$V_{B1}^d = \left( {1 - \alpha } \right)S\left[ {\frac{d}{{1 + r}} + \frac{{\left( {1 + r - d} \right) + \left( {u - 1 - r} \right){d^2}}}{{{{\left( {1 + r} \right)}^2}\left( {u - d} \right)}}} \right] - C$ (19)

根据上述t=T/2时的情况, $V_{A1}^u$ $V_{A1}^d$ 可以推出t=0时

${V_A} = V_{A1}^u \times {\text{上行概率}} + V_{A1}^d \times {\text{下行概率}}$ (20)
$\begin{aligned}{V_A} = & \left\{ {\alpha S\left[ {\frac{u}{{1 + r}} + \frac{{\left( {1 + r - d} \right){u^2} + \left( {u - 1 - r} \right)}}{{{{\left( {1 + r} \right)}^2}\left( {u - d} \right)}}} \right] - C} \right\} \times \frac{{1 + r - d}}{{u - d}}\\ & + \left\{ {\alpha S\left[ {\frac{d}{{1 + r}} + \frac{{\left( {1 + r - d} \right) + \left( {u - 1 - r} \right){d^2}}}{{{{\left( {1 + r} \right)}^2}\left( {u - d} \right)}}} \right] - C} \right\} \times \frac{{u - 1 - r}}{{u - d}}\\ = & \alpha S\Biggr[ \frac{{u\left( {1 + r - d} \right)}}{{\left( {1 + r} \right)\left( {u - d} \right)}} + \frac{{d\left( {u - 1 - r} \right)}}{{\left( {1 + r} \right)\left( {u - d} \right)}}\\& + \frac{{{{\left( {1 + r - d} \right)}^2}{u^2} + 2\left( {1 + r - d} \right)\left( {u - 1 - r} \right) + {{\left( {u - 1 - r} \right)}^2}{d^2}}}{{{{\left( {1 + r} \right)}^2}{{\left( {u - d} \right)}^2}}} \Biggr] - C\\ = & \alpha S\left( {1 + 1} \right) - C \quad = 2\alpha IC - C\end{aligned}$ (21)

同理,

${V_B} = 2\left( {1 - \alpha } \right)IC - C$ (22)

(2)A进行商业模式创新,B在期中t=T/2时模仿跟进,则

两期净现金流增长时,即uu

$V_{A2}^{uu} = \frac{{uS}}{{1 + r}} + \frac{{\alpha {u^2}S}}{{{{\left( {1 + r} \right)}^2}}} - C$ (23)
$V_{B2}^{uu} = \frac{{\left( {1 - \alpha } \right){u^2}S}}{{{{\left( {1 + r} \right)}^2}}}$ (24)

第一期净现金流增长,第二期降低,即ud

$V_{A2}^{ud} = \frac{{uS}}{{1 + r}} + \frac{{\alpha S}}{{{{\left( {1 + r} \right)}^2}}} - C$ (25)
$V_{B2}^{ud} = \frac{{\left( {1 - \alpha } \right)S}}{{{{\left( {1 + r} \right)}^2}}}$ (26)

第一期净现金流降低,第二期增长,即du

$V_{A2}^{du} = \frac{{dS}}{{1 + r}} + \frac{{\alpha S}}{{{{\left( {1 + r} \right)}^2}}} - C$ (27)
$V_{B2}^{du} = \frac{{\left( {1 - \alpha } \right)S}}{{{{\left( {1 + r} \right)}^2}}}$ (28)

两期净现金流都降低,即dd

$V_{A2}^{dd} = \frac{{dS}}{{1 + r}} + \frac{{\alpha {d^2}S}}{{{{\left( {1 + r} \right)}^2}}} - C$ (29)
$V_{B2}^{dd} = \frac{{\left( {1 - \alpha } \right){d^2}S}}{{{{\left( {1 + r} \right)}^2}}}$ (30)

根据上述t=T时情况,可以推出t=T/2时

$\begin{array}{l}V_{A1}^u = \left[ {\frac{{uS}}{{1 + r}} + \frac{{\alpha {u^2}S}}{{{{\left( {1 + r} \right)}^2}}} - C} \right] \times \frac{{1 + r - d}}{{u - d}} + \left[ {\frac{{uS}}{{1 + r}} + \frac{{\alpha S}}{{{{\left( {1 + r} \right)}^2}}} - C} \right] \times \frac{{u - 1 - r}}{{u - d}}\\\;\;\;\;\;\;\, = S\left[ {\frac{u}{{1 + r}} + \frac{{\alpha \left( {1 + r - d} \right){u^2} + \alpha \left( {u - 1 - r} \right)}}{{{{\left( {1 + r} \right)}^2}\left( {u - d} \right)}}} \right] - C\end{array}$ (31)
$\begin{array}{l}V_{B1}^u = \frac{{\left( {1 - \alpha } \right){u^2}S}}{{{{\left( {1 + r} \right)}^2}}} \times \frac{{1 + r - d}}{{u - d}} + \frac{{\left( {1 - \alpha } \right)S}}{{{{\left( {1 + r} \right)}^2}}} \times \frac{{u - 1 - r}}{{u - d}}\\\;\;\;\;\;\;\, = \left( {1 - \alpha } \right)S\left[ {\frac{{{u^2}\left( {1 + r - d} \right) + \left( {u - 1 - r} \right)}}{{{{\left( {1 + r} \right)}^2}\left( {u - d} \right)}}} \right]\end{array}$ (32)
$V_{A1}^d = S\left[ {\frac{d}{{1 + r}} + \frac{{\alpha \left( {1 + r - d} \right) + \alpha \left( {u - 1 - r} \right){d^2}}}{{{{\left( {1 + r} \right)}^2}\left( {u - d} \right)}}} \right] - C$ (33)
$V_{B1}^d = \left( {1 - \alpha } \right)S\left[ {\frac{{\left( {1 + r - d} \right) + \left( {u - 1 - r} \right){d^2}}}{{{{\left( {1 + r} \right)}^2}\left( {u - d} \right)}}} \right]$ (34)

根据上述t=T/2时的情况,可以推出t=0时

$\begin{aligned}{V_A} = & \left\{ {S\left[ {\frac{u}{{1 + r}} + \frac{{\alpha \left( {1 + r - d} \right){u^2} + \alpha \left( {u - 1 - r} \right)}}{{{{\left( {1 + r} \right)}^2}\left( {u - d} \right)}}} \right] - C} \right\} \times \frac{{1 + r - d}}{{u - d}}\\& + S\left\{ {\left[ {\frac{d}{{1 + r}} + \frac{{\alpha \left( {1 + r - d} \right) + \alpha \left( {u - 1 - r} \right){d^2}}}{{{{\left( {1 + r} \right)}^2}\left( {u - d} \right)}}} \right] - C} \right\} \times \frac{{u - 1 - r}}{{u - d}}\\= & \left[ {\left( {1 + \alpha } \right)I - 1} \right]C\end{aligned}$ (35)

同理,

${V_B} = \left( {1 - \alpha } \right)IC$ (36)

(3)B进行商业模式创新,A在期中t=T/2时模仿跟进,与情况(2)同理,可得

${V_A} = I\alpha C$ (37)
${V_B} = \left[ {\left( {2 - \alpha } \right)I - 1} \right]C$ (38)

(4)A、B都采取模仿策略,则VA=0,VB=0。

综上所述,可得如下博弈矩阵:

表 1 博弈矩阵
A企业 B企业
创 新 模 仿
创 新 $\left( {2\alpha I - 1} \right)C,\;\left[ {2\left( {1 - \alpha } \right)I - 1} \right]C$ $\left[ {\left( {1 + \alpha } \right)I - 1} \right]C,\;\left( {1 - \alpha } \right)IC$
模 仿 $I\alpha C,\;\left[ {\left( {2 - \alpha } \right)I - 1} \right]C$ 0,0
四、讨论分析

下面讨论四种策略组合的均衡情况:

(1)当(创新,创新)是纳什均衡解时,Iα须满足以下条件:

$\left\{ \begin{array}{l}\left( {2\alpha I - 1} \right)C > I\alpha C\\\left[ {2\left( {1 - \alpha } \right)I - 1} \right]C > \left( {1 - \alpha } \right)IC\end{array} \right.$ (39)

其中0<α<1,I>0。

解得:I>2, $\displaystyle\frac{1}{I} < \alpha < 1 - \displaystyle\frac{1}{I}$ ,即图3中阴影部分。

图 3  

推论1:T=0时基期净现金流基准S是商业模式创新投入C的2倍以上,且A企业市场份额要在 $\left( {\displaystyle\frac{1}{I},1 - \displaystyle\frac{1}{I}} \right)$ 之间,两个企业同时创新投入对两个企业来说才是均衡选择,基期基准倍数I越大,该策略下允许的市场份额差额 $\left( {1 - \displaystyle\frac{2}{I}} \right)$ 越大。

(2)当(创新,模仿)是纳什均衡解时,Iα须满足以下条件:

$\left\{ \begin{array}{l}\left[ {\left( {1 + \alpha } \right)I - 1} \right]C > 0\\\left( {1 - \alpha } \right)IC > \left[ {2\left( {1 - \alpha } \right)I - 1} \right]C\end{array} \right.$ (40)

其中0<α<1,I>0。

解得: $I > \displaystyle\frac{1}{2},{{max}}\left\{ {\displaystyle\frac{1}{I} - 1,1 - \displaystyle\frac{1}{I}} \right\} < \alpha < 1$ ,即图4中阴影部分。这说明α并不一定大于 $ \displaystyle\frac{1}{2}$ ,即有可能小企业创新,大企业模仿反而是均衡的。

图 4  

推论2a: $I \in \left( {\displaystyle\frac{2}{3},2} \right)$ ,且 ${{max}}\left\{ {\displaystyle\frac{1}{I} - 1,1 - \displaystyle\frac{1}{I}} \right\} < \alpha < \displaystyle\frac{1}{2}$ ,两个企业则出现市场份额较小的企业优先商业模式创新,大企业模仿跟进是均衡策略,Iα的限制区间如图4阴影部分1区所示。

推论2b: $I \in \left( {\displaystyle\frac{1}{2},\infty } \right)$ ,且 ${{max}}\left\{ {\displaystyle\frac{1}{I} - 1,1 - \displaystyle\frac{1}{I},\displaystyle\frac{1}{2}} \right\} < \alpha < 1$ ,两个企业则出现市场份额较大的企业优先商业模式创新,小企业模仿跟进是均衡策略,此时与“智猪博弈”的情况相符合,Iα的限制区间如图4阴影部分2区所示。

(3)当(模仿,创新)是纳什均衡解时,Iα须满足以下条件:

$\left\{ \begin{array}{l}I\alpha C > \left( {2\alpha I - 1} \right)C\\\left[ {\left( {2 - \alpha } \right)I - 1} \right]C > 0\end{array} \right.$ (41)

其中0<α<1,I>0。

解得: $I > \displaystyle\frac{1}{2},0 < {{\alpha }} < {{min}}\left\{ {2 - \displaystyle\frac{1}{I},\displaystyle\frac{1}{I}} \right\}$ ,即图5中阴影部分。这说明α并不一定小于 $ \displaystyle\frac{1}{2}$ ,即有可能小企业创新,大企业模仿反而是均衡的。

图 5  

推论3a: $I \in \left( {\displaystyle\frac{2}{3},2} \right)$ ,且 $\displaystyle\frac{1}{2} < {{\alpha }} < {{min}}\left\{ {2 - \displaystyle\frac{1}{I},\displaystyle\frac{1}{I}} \right\}$ ,两个企业则出现市场份额较小的企业优先商业模式创新,大企业模仿跟进是均衡策略,Iα的限制区间如图5阴影部分1区所示。

推论3b: $I \in \left( {\displaystyle\frac{1}{2},\infty } \right)$ ,且 $0 < {{\alpha }} < {{min}}\left\{ {2 - \displaystyle\frac{1}{I},\displaystyle\frac{1}{I},\displaystyle\frac{1}{2}} \right\}$ ,两个企业则出现市场份额较大的企业优先商业模式创新,小企业模仿跟进是均衡策略,此时与“智猪博弈”的情况相符合,Iα的限制区间如图5阴影部分2区所示。

(4)当(模仿,模仿)是纳什均衡解,即两个企业都不会率先进行创新,此时,Iα须满足以下条件:

$\left\{ \begin{array}{l}\left[ {\left( {1 + \alpha } \right)I - 1} \right]C < 0\\\left[ {\left( {2 - \alpha } \right)I - 1} \right]C < 0\end{array} \right.$ (42)

其中0<α<1,I>0。解得: $0 < I < \displaystyle\frac{2}{3}$ $ \max \left\{ {0.2 - \displaystyle\frac{1}{I}} \right\} < \alpha < \min \left\{ {1,\displaystyle\frac{1}{I} - 1} \right\},$ 图6阴影部分。

图 6  

推论4: $I \in \left( {0,\displaystyle\frac{1}{2}} \right)$ ,不管份额如何,两企业都不会选择商业模式创新,因为商业模式创新的收益太低了;当 $I \in \left( {\displaystyle\frac{1}{2},\displaystyle\frac{2}{3}} \right)$ ,且 $2 - \displaystyle\frac{1}{I} < \alpha < \displaystyle\frac{1}{I} - 1$ ,两企业也不会选择进行商业模式创新,因为任何一方进行商业模式创新都是“便宜”了另一方。

综上讨论,可以知道企业进行商业模式创新和模仿决策时不仅仅是“智猪博弈”,由于基期基准倍数和市场份额的不同,会产生不同的均衡策略。如图7所示,当Iα的限制区间在A区时,两企业选择同时进行商业模式创新是均衡策略;当在B区时,小企业创新,大企业模仿反而是均衡策略;但在C区时,大企业创新,小企业模仿跟进是均衡策略,此时符合“智猪博弈”的均衡结果;当在D区时,由于收益率过低和不管谁创新都会有利于另一方,导致都不进行创新是此时的均衡策略。

图 7  
五、结论和展望

一方面,由于缺少法律明确定位,我国仍然没能解决“互联网商业模式能否申请专利,以及如何申请专利”等问题,这就导致商业模式被模仿的现象尤为常见;另一方面,商业模式创新又是企业获得更多收益的重要手段,Mitchell和Coles(2003)认为商业模式不断创新才能摆脱竞争者的模仿,所以企业并不只在创立之初进行商业模式创新,商业模式变动在企业生命周期是时常发生的。而每次创新都可能要面临创新投入、收益不确定性和竞争者的模仿,本文将这种普遍现象提炼出来,综合了这三个因素,构建实物期权博弈模型解决企业进行商业模式改变时的较优决策问题。

通过讨论分析,得出以下几个结论:

(1)企业的风险取决于收益不确定性的大小,然而在创新—模仿博弈中,不确定性对企业的策略选择没有影响,真正起决定作用的是市场份额和基期基准倍数,这是因为不确定性不会对某企业特殊,竞争者承担同样的风险。

(2)“智猪博弈”无法完整解释企业商业模式创新—模仿决策问题,(创新,创新)、(创新,模仿)、(模仿,创新)、(模仿,模仿)四种均衡决策会随着基期基准倍数I和市场份额α的不同都有可能出现。当收益率很高即基期基准倍数很高(I>2)且两个市场份额差额在 $1 - \displaystyle\frac{2}{I}$ 以内时,(创新,创新)是最优选择;当基期基准倍数较高 $I \in \left( {\displaystyle\frac{2}{3},2} \right)$ 且两企业市场份额较接近 $\left( {\max \left\{ {\displaystyle\frac{1}{I} - 1,1 - \displaystyle\frac{1}{I}} \right\} < \alpha < {{min}}\left\{ {2 - \displaystyle\frac{1}{I},\displaystyle\frac{1}{I}} \right\}} \right)$ ,则会出现小企业创新,大企业模仿的均衡策略,这种情况否定了“智猪博弈”;当基期基准倍数不低 $I \in \left( {\displaystyle\frac{1}{2},\infty } \right)$ 且两企业市场份额相差较大(如图7中C区)时,大企业创新,小企业模仿是最优选择,结论与“智猪博弈”吻合;最后,当收益率很低时I $ \in \left( {0,\displaystyle\frac{2}{3}} \right)$ 时,两个企业都应该放弃商业模式创新。

和前人的研究相比,本文有两个主要创新点。在商业模式创新领域,学术界完成理论概念构建、量表开发和实证探究几个阶段(Zott等,2011;Zott和Amit,2007),研究内容主要是商业模式创新能给企业绩效带来的影响(Aspara等,2010;Kastalli和Van Looy,2013)。从数理模型和博弈论思想来分析商业模式创新的价值非常少,我们采用实物期权博弈来评估创新和模仿的价值是一个比较新的视角。商业模式创新是一个系统性的变革(Velu,2015),比一般项目投资更加复杂,而实物期权博弈突出对不确定性和对手决策的考量更加符合现实情景。另一方面,现有关于实物期权的研究多采用Black-Scholes的期权定价的方法,属于欧式期权,但现实中,像商业模式创新这种投资,企业获得收益是在整个项目期间持续的,属于美式期权(Copeland,2015),所以我们采用二叉树定价法可以将项目期间收益纳入考量,为以后的研究拓展提供一个方向性的基础。

在理论层面,本文首先丰富了商业模式创新价值评估的研究,我们在分析中考察了不确定性和竞争对手选择的影响,对这一领域的价值模型建构具有学术贡献,一定程度上弥补了概念构建和实证探究两种研究方法的不足。其次,本文拓展了实物期权方法的运用,结合商业模式创新和模仿的特征,我们根据二叉树期权定价的逻辑建构了本文的两期二叉树模型,为学术研究中解决类似问题提供了一些借鉴。另外,本文分析结论能为管理实践提供启示,新的模型能够解释一些基本现象,管理者在决定商业模式创新或模仿策略时需要考量初期的市场基础和与竞争者的规模差别。

现有文献中有关企业进行投资分析、商业模式收益预测时仍普遍使用NPV方法,实物期权博弈并没有被分析者广泛运用,需要更多的研究者不断丰富完善该方法,以期其在实践中有更加合理的运用。未来,我们期望相关研究能在以下几个方面有所突破。首先,当考虑多个参与者和多个策略选择时,问题将变得更复杂,也更加接近现实情况。突破二元选择时,二叉树方法将不再适用,数学上的概率分布和随机游走也能在实物期权领域的分析发挥巨大作用。其次,另一项复杂的工作是关于实物期权中不确定性的衡量,存在风险的因素有很多,将其统一成一个变量还是独立多个变量综合分析将是学者未来一个研究方向。最后,需要更多的实证数据和案例分析来证明实物期权方法在实践中的正确性,验证其在预测上优于传统NPV方法。

本文虽然为实物期权具体实践运用迈出了一小步,但由于模型是基于理想化的假设,在实际使用中存在一定局限性:(1)两期模型是一个理想化的情况,实际上模仿者跟进的时间往往不是在项目中期。将模型拓展至模仿者任意时间跟进是未来的一个研究方向,其结果将更具有实际意义。(2)模型假设了创新不带来市场份额的变化,该前提假设在平台型企业中较为常见,意味着创新者会考量模仿者进入后对份额的侵蚀,并合理控制变动成本使得在净现金流分配时按原份额分成。实际上创新以及后期投入会带来市场份额的变动,未来研究将针对创新—模仿博弈设计份额变动动态过程以期还原实际竞争情况。

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