自我控制、上瘾与纵向差异化竞争
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摘要
鉴于自我控制问题所导致的消费者上瘾行为在我国诸多产业中的普遍存在,将易上瘾产品的习惯形成性与负的内部性引入到企业的纵向差异化价格竞争中,考察了自我控制问题的严重程度不同的消费者下企业的定价策略,并对各行为类型消费者下的企业均衡价格与市场份额进行了对比分析.研究表明,在理性消费者情形下,企业的纵向差异化竞争只存在唯一的均衡;而当消费者存在自我控制问题时,则竞争可能存在多种均衡可能性,这是由消费者的自我控制问题所导致的过度自信或心理成熟所造成的.同时,消费者对两企业产品的体验水平组合对企业的纵向差异化的均衡价格和市场份额产生影响,而且消费者在消费两企业产品时的负内部性与习惯形成性的大小也会影响企业的竞争均衡.
Since the addiction induced by consumer's self-control problems is prevalent in many Chinese industries,this paper introduces two features of addiction proposed by O'Donoghue and Rabin(1999 a,2002) :habit-forming and negative internalities,into duopolistic price competition with vertical differentiation.Firms' equilibrium pricing strategies are investigated when consumers are rational,naive and sophisticated,and the equilibrium price of each firm and the corresponding market share with each other in these three cases are also compared.It is found that when consumers are rational,price competition generates a unique equilibrium.By contrast,when consumers are quasi-hyperbolic discounters,the competition between firms may have multiple equilibria,which attributes to consumers' overconfidence in their future consumptions or sophistication.Meanwhile,under each of the three behavioral types of consumers,three factors will affect the firms' equilibrium prices and corresponding market shares:the consumer's initial experience portfolio of the two addictive products,the parameter of habit-forming,and the size of negative internalities.
Since the addiction induced by consumer's self-control problems is prevalent in many Chinese industries,this paper introduces two features of addiction proposed by O'Donoghue and Rabin(1999 a,2002) :habit-forming and negative internalities,into duopolistic price competition with vertical differentiation.Firms' equilibrium pricing strategies are investigated when consumers are rational,naive and sophisticated,and the equilibrium price of each firm and the corresponding market share with each other in these three cases are also compared.It is found that when consumers are rational,price competition generates a unique equilibrium.By contrast,when consumers are quasi-hyperbolic discounters,the competition between firms may have multiple equilibria,which attributes to consumers' overconfidence in their future consumptions or sophistication.Meanwhile,under each of the three behavioral types of consumers,three factors will affect the firms' equilibrium prices and corresponding market shares:the consumer's initial experience portfolio of the two addictive products,the parameter of habit-forming,and the size of negative internalities.
引文
[1]Becker G S,Murphy K M.A theory of rational addiction[J].Journal of Political Economy,1988,96(4):675-700.
[2]O'Donoghue T,Rabin M.Addiction and self-control[C].In Addiction:Entries and Exits,Jon Elster,editor,Russel Sage Foundation,1999a.
[3]O'Donoghue T,Rabin M.Addiction and Present-biased Preferences[R].Working Paper,Ithaca:Cornell University,2002.
[4]杨剑侠,陈宏民,包兴.网络游戏运营商利用消费者的上瘾行为定价了吗?来自中国网络游戏产业的证据[J].《经济学(季刊)》,2009,8(4):1329-1382.Yang Jianxia,Chen Hongmin,Bao Xing.Have service providers taken advantage of consumer's addiction in their pricing strategies?Evidence from Chinese online games[J].China Economic Quarterly,2009,8(4):1329-1382.(in Chinese)
[5]Becker G S,Grossman M,Murphy K M.An empirical analysis of cigarette addiction[J].American Economic Review,1994,84(3):396-418.
[6]Orphanides A,Zervos D.Rational addiction with learning and regret[J].Journal of Political Economy,1995,103(4):739-758.
[7]Wang R.The optimal consumption and the quitting of harmful addictive goods[J].The B.E.Journal of Economic Analysis&Policy,2007,7(1):1-36.
[8]Dragone D,Manaresi F,Savorelli L.Multiple Rational Addiction and the Effect of Price on Consumption[R].Working Paper,Bologna:University of Bologna,2016.
[9]Reif J.A Model of Addiction and Social Interactions[R].Working Paper,Champaign:University of Illinois at UrbanaChampaign,2017.
[10]Carrillo J.To be consumed with moderation[J].European Economic Review,2005,49:99-111.
[11]Gruber J,Koszegi B.Is addiction rational?Theory and evidence[J].Quarterly Journal of Economics,2001,116(4):1261-1303.
[12]Gul F,Pesendorfer W.Harmful addiction[J].Review of Economic Studies,2007,74(1):147-172.
[13]Levy M.An Empirical Analysis of Biases in Cigarette Addiction[R].Working Paper,Cambridge:Harvard University,2010.
[14]Bernheim B D,Rangel A.Addiction and cue-triggered decision processes[J].American Economic Review,2004,94(5):1558-1590.
[15]Gruber J,Koszegi B.Tax incidence when individuals are time-inconsistent:The case of cigarette excise taxes[J].Journal of Public Economics,2004,88(9-10):1959-1987.
[16]Gordon B R,Sun B.A dynamic model of rational addiction:Evaluating cigarette taxes[J].Marketing Science,2015,34(3):452-470.
[17]Showalter M H.Firm behavior in a market with addiction:The case of cigarettes[J].Journal of Health Economics,1999,18(4):409-427.
[18]杨剑侠,陈宏民,孙武军.自我控制、上瘾与最优定价:理论与经验证据[J].管理科学学报,2013,16(11):1-16.Yang Jianxia,Chen Hongmin,Sun Wujun.Self-control,addiction and optimal pricing:Theory and evidence[J].Journal of Management Sciences in China,2013,16(11):1-16.(in Chinese)
[19]Baake P,Boom A.Vertical product differentiation,network externalities and compatibility decisions[J].International Journal of Industrial Organization.2001,19(1-2):267-284.
[20]Economides N,Mitchell M,Skrzypacz A.Dynamic Oligopoly with Network Effects[R].Working Paper,New York:New York University,2005.
[21]Hend G,Rim L.Vertical Differentiation,Network Externalities and Compatibility Decisions:An Alternative Approach[R].Working Paper,Paris:University of Paris,2006.
[22]Boccard N,Wauthy X.Equilibrium vertical differentiation in a Bertrand model with capacity precommitment[J].International Joumal of Industrial Organization,2010,28(3):288-297.
[23]Bergemann D,Vlimki J.Entry and vertical differentiation[J].Journal of Economic Theory,2002,106(1):91-125.
[24]Narajabad B,Watson R.A Dynamic Duopoly with Endogenous Horizontal and Vertical Differentiation[R].Working Paper,Austin:University of Texas at Austin,2007.
[25]Phelps E S,Pollak R A.On second-best national saving and game-equilibrium growth[J].Review of Economic Studies,1968,35(2):185-199.
[26]Laibson D.Hyperbolic discounting and golden eggs[J].Quarterly Journal of Economics,1997,112(2):443-477.
[27]O'Donoghue T,Rabin M.Doing it now or later[J].American Economic Review,1999b,89(1):103-124.
[28]O'Donoghue T,Rabin M.Choice and procrastination[J].Quarterly Journal of Economics,2001,116(1):121-160.
[29]Gul F,Pesendorfer W.Temptation and self-control[J].Econometrica,2001,69:1403-1436.
[30]Eliaz K,Spiegler R.Contracting with diversely naive agents[J].Review of Economic Studies,2006,73(3):689-714.
[31]蒋军锋,曲霞.个体行为与自我控制:一个理论综述[J].经济研究,2016,9:162-174.Jiang Junfeng,Qu Xia.A summary of theories on individual behavior and self-control[J].Economic Research Journal,2016,9:162-174.(in Chinese)
(2)表中的相对实际上瘾指数是指杨剑侠等[4]的30款游戏中各游戏的实际上瘾指数与其中的最大值的比值.而表中每款游戏的实际上瘾指数是由下文的r=0.998时计算得到.实际上瘾指数越高,玩家对游戏就越上瘾.
(3)杨剑侠等[4]对我国30款网络游戏的玩家上瘾行为进行了实证研究,不仅发现有相当部分的上瘾玩家存在自我控制问题,而且还发现他们大多数是心理成熟型的,并校准出了对应的短期折现因子.
(4)文中的体验水平等同于O'Donoghue和Rabin[2,3]的上瘾水平(addiction level).
(5)在度量消费者的长期效用时,这里采用了O'Donoghue和Rabin[28]建议的长期偏好标准,也即从1期的自我角度出发,当消费者在第1期不存在自我控制问题时所获得的跨期总效用.该标准是一个事前标准,反映了消费者所获得的跨期效用与其的长期利益目标相一致的.
(6)关于边际成本的假设遵循了现有的纵向差异化竞争的理论文献,包括Bergemann和Vlimki[23],Boccard和Wauthy[22],Hend和Rim[21],以及Narajabad和Watson[24]等.
(7)以TC型消费者为例,为了保证在均衡价格下即使初始体验水平k A1和k B1均为0,类型为θ-的消费者也会在第一期购买企业A或B的产品进行消费,则要求:θ-≥θ-tc=max3c+2θ(q A-q B)+δ(2ΔH A+ΔH B)(4q A-q B),3c+θ(q A-q B)+δ(ΔH A+2ΔH B)(2q A+q B{}),类似的,对幼稚型与成熟型消费者,也能得到对应的θ-n和θ-s.于是,只要满足条件θ-≥max{θ-tc,θ-n,θ-s},市场在任何行为类型消费者下都能够被覆盖.
(8)O'Donoghue和Rabin[3]的单调消费策略是指当能免费消费某个产品时,在静态偏好模型下,TC消费者或心理幼稚型消费者在任何一个时期选择消费行为当且仅当其此时的体验水平不低于某一个临界的体验水平.因此,只要在某一个其的体验水平不低于该临界体验水平,则其以后必然每期都消费该产品.
(9)此时心理成熟型消费者可能的最优消费策略有以下几种:第一,视其具体的体验水平组合的情况而消费产品A从一次(或一个单位)到有限多次不等,而且若消费次数超过一次,则这些消费行为是连续发生的;第二,视其具体的体验水平组合的情况而先消费产品A若干期,然后又消费产品B若干期,如此周期性的消费;第三,完全不遵守逆向一刀切的消费策略,而且也不采用周期性消费产品A的方式,而是采用非周期性的能够达到理想消费次数的消费策略等.
(10)即使考虑了直接网络外部性或者交叉网络外部性,该结论也是成立的.
(11)根据式(11)和式(12)中企业A和企业B的最优价格,可以得到p tc*A
[2]O'Donoghue T,Rabin M.Addiction and self-control[C].In Addiction:Entries and Exits,Jon Elster,editor,Russel Sage Foundation,1999a.
[3]O'Donoghue T,Rabin M.Addiction and Present-biased Preferences[R].Working Paper,Ithaca:Cornell University,2002.
[4]杨剑侠,陈宏民,包兴.网络游戏运营商利用消费者的上瘾行为定价了吗?来自中国网络游戏产业的证据[J].《经济学(季刊)》,2009,8(4):1329-1382.Yang Jianxia,Chen Hongmin,Bao Xing.Have service providers taken advantage of consumer's addiction in their pricing strategies?Evidence from Chinese online games[J].China Economic Quarterly,2009,8(4):1329-1382.(in Chinese)
[5]Becker G S,Grossman M,Murphy K M.An empirical analysis of cigarette addiction[J].American Economic Review,1994,84(3):396-418.
[6]Orphanides A,Zervos D.Rational addiction with learning and regret[J].Journal of Political Economy,1995,103(4):739-758.
[7]Wang R.The optimal consumption and the quitting of harmful addictive goods[J].The B.E.Journal of Economic Analysis&Policy,2007,7(1):1-36.
[8]Dragone D,Manaresi F,Savorelli L.Multiple Rational Addiction and the Effect of Price on Consumption[R].Working Paper,Bologna:University of Bologna,2016.
[9]Reif J.A Model of Addiction and Social Interactions[R].Working Paper,Champaign:University of Illinois at UrbanaChampaign,2017.
[10]Carrillo J.To be consumed with moderation[J].European Economic Review,2005,49:99-111.
[11]Gruber J,Koszegi B.Is addiction rational?Theory and evidence[J].Quarterly Journal of Economics,2001,116(4):1261-1303.
[12]Gul F,Pesendorfer W.Harmful addiction[J].Review of Economic Studies,2007,74(1):147-172.
[13]Levy M.An Empirical Analysis of Biases in Cigarette Addiction[R].Working Paper,Cambridge:Harvard University,2010.
[14]Bernheim B D,Rangel A.Addiction and cue-triggered decision processes[J].American Economic Review,2004,94(5):1558-1590.
[15]Gruber J,Koszegi B.Tax incidence when individuals are time-inconsistent:The case of cigarette excise taxes[J].Journal of Public Economics,2004,88(9-10):1959-1987.
[16]Gordon B R,Sun B.A dynamic model of rational addiction:Evaluating cigarette taxes[J].Marketing Science,2015,34(3):452-470.
[17]Showalter M H.Firm behavior in a market with addiction:The case of cigarettes[J].Journal of Health Economics,1999,18(4):409-427.
[18]杨剑侠,陈宏民,孙武军.自我控制、上瘾与最优定价:理论与经验证据[J].管理科学学报,2013,16(11):1-16.Yang Jianxia,Chen Hongmin,Sun Wujun.Self-control,addiction and optimal pricing:Theory and evidence[J].Journal of Management Sciences in China,2013,16(11):1-16.(in Chinese)
[19]Baake P,Boom A.Vertical product differentiation,network externalities and compatibility decisions[J].International Journal of Industrial Organization.2001,19(1-2):267-284.
[20]Economides N,Mitchell M,Skrzypacz A.Dynamic Oligopoly with Network Effects[R].Working Paper,New York:New York University,2005.
[21]Hend G,Rim L.Vertical Differentiation,Network Externalities and Compatibility Decisions:An Alternative Approach[R].Working Paper,Paris:University of Paris,2006.
[22]Boccard N,Wauthy X.Equilibrium vertical differentiation in a Bertrand model with capacity precommitment[J].International Joumal of Industrial Organization,2010,28(3):288-297.
[23]Bergemann D,Vlimki J.Entry and vertical differentiation[J].Journal of Economic Theory,2002,106(1):91-125.
[24]Narajabad B,Watson R.A Dynamic Duopoly with Endogenous Horizontal and Vertical Differentiation[R].Working Paper,Austin:University of Texas at Austin,2007.
[25]Phelps E S,Pollak R A.On second-best national saving and game-equilibrium growth[J].Review of Economic Studies,1968,35(2):185-199.
[26]Laibson D.Hyperbolic discounting and golden eggs[J].Quarterly Journal of Economics,1997,112(2):443-477.
[27]O'Donoghue T,Rabin M.Doing it now or later[J].American Economic Review,1999b,89(1):103-124.
[28]O'Donoghue T,Rabin M.Choice and procrastination[J].Quarterly Journal of Economics,2001,116(1):121-160.
[29]Gul F,Pesendorfer W.Temptation and self-control[J].Econometrica,2001,69:1403-1436.
[30]Eliaz K,Spiegler R.Contracting with diversely naive agents[J].Review of Economic Studies,2006,73(3):689-714.
[31]蒋军锋,曲霞.个体行为与自我控制:一个理论综述[J].经济研究,2016,9:162-174.Jiang Junfeng,Qu Xia.A summary of theories on individual behavior and self-control[J].Economic Research Journal,2016,9:162-174.(in Chinese)
(2)表中的相对实际上瘾指数是指杨剑侠等[4]的30款游戏中各游戏的实际上瘾指数与其中的最大值的比值.而表中每款游戏的实际上瘾指数是由下文的r=0.998时计算得到.实际上瘾指数越高,玩家对游戏就越上瘾.
(3)杨剑侠等[4]对我国30款网络游戏的玩家上瘾行为进行了实证研究,不仅发现有相当部分的上瘾玩家存在自我控制问题,而且还发现他们大多数是心理成熟型的,并校准出了对应的短期折现因子.
(4)文中的体验水平等同于O'Donoghue和Rabin[2,3]的上瘾水平(addiction level).
(5)在度量消费者的长期效用时,这里采用了O'Donoghue和Rabin[28]建议的长期偏好标准,也即从1期的自我角度出发,当消费者在第1期不存在自我控制问题时所获得的跨期总效用.该标准是一个事前标准,反映了消费者所获得的跨期效用与其的长期利益目标相一致的.
(6)关于边际成本的假设遵循了现有的纵向差异化竞争的理论文献,包括Bergemann和Vlimki[23],Boccard和Wauthy[22],Hend和Rim[21],以及Narajabad和Watson[24]等.
(7)以TC型消费者为例,为了保证在均衡价格下即使初始体验水平k A1和k B1均为0,类型为θ-的消费者也会在第一期购买企业A或B的产品进行消费,则要求:θ-≥θ-tc=max3c+2θ(q A-q B)+δ(2ΔH A+ΔH B)(4q A-q B),3c+θ(q A-q B)+δ(ΔH A+2ΔH B)(2q A+q B{}),类似的,对幼稚型与成熟型消费者,也能得到对应的θ-n和θ-s.于是,只要满足条件θ-≥max{θ-tc,θ-n,θ-s},市场在任何行为类型消费者下都能够被覆盖.
(8)O'Donoghue和Rabin[3]的单调消费策略是指当能免费消费某个产品时,在静态偏好模型下,TC消费者或心理幼稚型消费者在任何一个时期选择消费行为当且仅当其此时的体验水平不低于某一个临界的体验水平.因此,只要在某一个其的体验水平不低于该临界体验水平,则其以后必然每期都消费该产品.
(9)此时心理成熟型消费者可能的最优消费策略有以下几种:第一,视其具体的体验水平组合的情况而消费产品A从一次(或一个单位)到有限多次不等,而且若消费次数超过一次,则这些消费行为是连续发生的;第二,视其具体的体验水平组合的情况而先消费产品A若干期,然后又消费产品B若干期,如此周期性的消费;第三,完全不遵守逆向一刀切的消费策略,而且也不采用周期性消费产品A的方式,而是采用非周期性的能够达到理想消费次数的消费策略等.
(10)即使考虑了直接网络外部性或者交叉网络外部性,该结论也是成立的.
(11)根据式(11)和式(12)中企业A和企业B的最优价格,可以得到p tc*A
(1 -δ)(-1)(ΔH A k A1-ΔH B k B1).
(12)当存在网络外部性但企业之间的产品完全兼容时,企业的均衡价格与无网络外部性时相同,且在θ>2θ时有p*A>p*B.而当两企业的产品完全不兼容时,相同的结论仍然成立.
(13)因为消费者认为自己从下一期开始就不消费企业A的产品了,从而也就不能在以后享受到应有的补偿,所以企业A必须一次性的给予补偿才能吸引消费者.
(14)因为给定消费者的初始体验水平组合,此时企业的最优定价策略可能使得部分消费者的最优消费路径为消费产品A有限次,然后再消费产品B;反之亦然。由于此时消费者完全不需要遵守所谓的“单调消费策略”或“一刀切消费策略”(cutoff strategy),从而使得企业的定价行为也变得十分复杂,甚至不存在纯策略均衡。这就无法提供有意义的经济学洞察。此外,复杂的定价策略本身也难以与相应产业中企业价格竞争的现实匹配.
(15)该均衡之所以不存在,是由于θ^IE AB不存在.因为根据定义,θ^IE AB只可能在ρA-ρB≥0且ρB-ρA<0时存在,或在ρA-ρB<0且ρB-ρA≥0时存在.第一种情况要求βδ(ΔH B-ΔH A)=(-1)(ρA+ρB)/(1-γ),而第二种情况要求βδ(ΔH A-ΔH B)=(-1)(ρA+ρB)/(1-γ).通过简单分析可知,这些要求都与θ^IE AB存在的前提条件相矛盾.因此,θ^IE AB不存在,对应的定价均衡也就不存在.
(16)《航海世纪》在2006年9月22日已经全面免费运营。目前为止,在我国运营的免费网络游戏已经达到300款以上.我国网络游戏的免费运营,以2005年11月网络游戏《热血传奇》和《传奇世界》的免费运营最为业界所重视.免费网络游戏对玩家免费开放,但是游戏中的虚拟道具或者说装备是收费的,而且实质上所受的费用经过折算可能比原来的收费价格更高.其本质上是一种变相的收费模式.