Competitive Innovation Diffusion in Small-World Network: Agent-Based Modeling and Simulation *

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1 Technology and Invesmen, 2012, 3, hp://dx.doi.org/ /i Published Online Augus 2012 (hp:// Compeiive Innovaion Diffusion in Small-World Nework: Agen-Based Modeling and Simulaion * Yunfeng Yan, Ying Li Deparmen of Managemen Science and Engineering, School of Business, Eas China Universiy of Science and Technology, Shanghai, China liying@ecus.edu.cn Received July 10, 2012; revised Augus 10, 2012; acceped Augus 17, 2012 ABSTRACT The main purpose of his paper is o analyze he dynamic process when wo compeiive innovaions diffuse simulaneously in he small world nework. To illusrae he micro diffusion process, an agen-based modeling and simulaion mehod is applied. In he agen based model, here are wo compeiive innovaions. Agens make decisions o adop one of he innovaions according o he uiliy value. The sensiiviy of he parameers of he uiliy funcion is analyzed. The resul indicaes ha in he early sage and he lae sage he adverisemen sraegy is beer; while in he middle sage he word-of-mouh will be beer. Keywords: Small-World Nework; Innovaion Diffusion; Compeiive Innovaions; Diffusion Model 1. Inroducion Innovaion could be a produc, a mehod or a heory. To he innovaion adopers, innovaion diffusion is a slow process, which depends on he nework and he diffusion. Jus like Rogers [1] said, innovaion is he process which propagaes among he social sysem members in a specific channel over ime. He also poins ou ha he innovaion diffusion process is made of four key acors: innovaion, informaion channel, ime and social sysem. Innovaion diffusion heory is mainly focus on which channel he new echnology propagaed. The compeiion is a mus in he innovaion diffusion in he real work under he marke mechanism. A he same ime, many replaceable innovaions may occur. Many researches are on he compeiive innovaion diffusion, whaever in or ou China. Reccardo L. [2] sudied he marke segmenaion mechanism in he same marke for wo producs and validaed i by a digial experimen. Chihiro Waanabe [3] sudied he replace orbi in innovaion replacemen by he uilizaion of L-V model and does he empirical sudy on he diffusion of he digial TV in Japanese. In China, sudied he compeiion and diffusion for wo producs and did he empirical sudy in Chinese communicaion marke [4,5]. According o he relaionship of he producs and echnology, he compei- * This paper is funded by Naural Science Foundaion of Shanghai (09ZR ), Naural Science Fund of China ( ), Social Science Fund of Chinese Minisry of Educaion (09YJC630069), and Naional Science Fund for Disinguished Young Scholars ( ). ive innovaion models can be divided ino: compeiive models, complemenarily models, replaceable models and echnology innovaion models [6]. The model we consruced in his paper is a replaceable model. A he same ime, here are wo innovaions exis in he marke. They are compeiive producs. The purpose of his paper is o analyze which facors will influence he compeiive diffusion and he effec of he word of mouh and he adverisemen. 2. Compeiive Diffusion Model All he innovaion diffusions need he diffusion medium. Generally, innovaion diffusion is in a specific nework. Many neworks in he real social, for example, finance marke, personal relaionships, Indusrial clusers [7] and so on, are us like wha Was and Srongaz [8] said he small world neworks. So i is meaningful o analyze he diffusion in small world neworks. The nework applied in his paper is he small world nework which conains 1000 nodes. There are wo and only wo innovaions in he model. And a he sar of he diffusion, he marke share for each innovaion is differen in order o invesigae how lower one o cach up wih he higher ones Diffusion Model for a Single Innovaion The componen of our model is derived from he model in reference [9]. In he model, here are a se of acors who differ in he social ies, and hey make decisions o

2 Y. F. YAN, Y. LI 199 adop or reec an innovaion. A each ime sep every acor has o decide wheher o adop he innovaion, or if already adoped, wheher o give up i. Each acor s decision is based on (a) his/her aiude owards he innovaion and (b) he adopion behavior of his/her social nework. Two hresholds are assigned o each agen. The firs hreshold L governs adopion; he second hreshold R is always a fixed fracion of he firs and governs he giving up of he adopion of he innovaion. Also, he agens have heir memory. In his way hey can make heir adopion decision based on heir percepion of how well his innovaion has been esablished in he pas. To ake he observed rend in innovaion use ino accoun we define an acor a s personal nework rend as he weighed sum of: 1) The average number of adopers in a s personal nework and; 2) The average gain/loss of adopers wihin a s nework over a period of en ime seps. If a s personal nework rend exceeds a s hreshold for adopion, a will adop; if his degree falls below a s hreshold for giving up he adopion, a will give up adoping he innovaion. The memory ha allows acors o ake rends ino consideraion and he hreshold for giving up adopion disinguish our model from oher hreshold models 3. These componens, as we shall see, enable our acors o give up adoping an innovaion. E W d 10 W d 1 d i 9 1 i 2 M W3N 1 A W mn 4 1 i where, W 1 means he weigh for he average number of adopers in a personal nework; W 2 means he weigh for average gain/loss of adopers in personal ne (observed rend). In his paper, we add wo facors: 1) he word of mouh M, which means he innovaion adopers evaluaion on he innovaion, he effec of word of mouh is in direc proporion o m; and 2) he adverisemen A, which is like he public medium in BASS model. The adverisemen is in direc proporion o (m N ). where, W 3 means word of mouh coefficien, which can be changed by adus he W 3. Iem (m N 1 ) means he (1) (2) number of he adopers who have no adoped he innovaion. W 4 is adverisemen coefficien, which can be changed by he change of W 4. The uiliy value o each innovaion for each node in model is no only relaed o he number of he node s neighbor in 10 seps, bu also relaed o innovaion diffusion rend and word of mouh and adverisemen. More specifically, he uiliy value of node in ime is shown in Equaion (3). Nex, we will simulae he compeiive innovaions diffusion in he small world nework. For innovaion A and B, we assume A has higher marke share a he beginning of he simulaion Two Compeiive Innovaions Diffusion Model 1) Model Assumpions For each agen, i could have one of he hree sauses a ime : S () = 0 means node adops no innovaion. S () = 1 means node adop innovaion A. S () = 2 means node adop innovaion B. We have he assumpions below in he wo compeiive innovaions model: There are wo innovaions A and B in he nework and hey are replaceable; A he beginning of he simulaion, he marke share of A is higher han B; The saus of a node can be 0, 1, or 2. A node can only have one saus in a ime; The nodes can adop or drop he innovaions. 2) The Procedure of Innovaion Diffusion The nodes accep or drop he innovaion depends on he uiliy value E. If E is bigger han hreshold value L, he node adops he node. If E is smaller han refuse hreshold (R L), he node drop he node. The udgmen funcion is shown in Table 1. From he Table 1, we can see: in he diffusion process, when S ( 1) = 0, if E A > L, hen S () = 1; else S () = 0. When S ( 1) = 1, if E A R L, S () = 1; else S () = 0. The simulaion flow char is shown in Figure Simulaion Resuls We se marke share of A is bigger han B. And he diffusion D W1 M A 1 D i D D i i i i E W1 W2 M A 1,10 1 D 9D 1 Di i 9 i i i W1 W2 M A (3)

3 200 Y. F. YAN, Y. LI S 1 S Table 1. Decision model. 0, EA LEB L 10 1, EA EB EA L 2, EB EA EB L 0, EA RL EB L 11 1, EA RL 2, EA EB EB LE RL A 0, EB RL EA L 12 1, EB RL 2, EB EA EA LE RL B Sar =1 Se he iniial diffusion origins A={n1,n2,n3,n4 } i=1, =1 =Max no. of simulaion End Search all he nodes conneced wih A(i), and add hem ino ser Q i++ =1 ++ i<=lengh(a) <=lengh(q) Calculae Q() s E A, and check he value of Q() s saus S(-1) S(-1)=2 S(-1) S(-1)=0 E A >E B, Q() s S()=1; E A <E B, Q() s S=2; E A =E B,Q() s S()choose 1or 2 randomly S(-1)=1 E A <(R L), o Q(), S()=0, else S()=1 If S() S(-1), add Q()o se A,++ E A >L, o Q(), S()=1, else S()=0 Figure 1. Flow char of he simulaion algorihm. poin of A is 8 and of B is 4. The res parameers is W 1A = 0.3; W 1B = 0.3; W 2A = 0.7; W 2B = 0.7; W 3A = 0.1; W 3B = 0.1; W 4A = 0.2; W 4B = 0.2; R = 0.5; L = The Sensiive Analysis of W 1 Then we change he value of W 1 o check how W 1 influence he diffusion. W 1 is he one o influence he Inno- vaion Perceive. The bigger he W 1, he bigger he innovaion perceive. We hen change W 1 from 0.25 o The increase sep is The resul is shown in Figure 1. According o he Figure 2, A s iniial marke share is higher han s. So in he early sage of he diffusion, A s marke share is higher han s. In he middle sage of he diffusion, when A is in sauraion, B is going on growing. So finally he number of nodes who adop B is bigger

4 Y. F. YAN, Y. LI 201 han A s (Blue line is for A and green dashed is for B). Then we increase W 1. When W 1 = 0.27, innovaion A increased rapidly and exceeded B a las (Red line is for A when purple dashed is for B). Keep increasing A, when W 1 = 0.29, A s and B s nodes become more. Bu he exen is less (Black line is for A and ligh blue dashed is for B). From he resul above, we can conclude ha a he beginning, he innovaion perceive is lile. And A is sroke ino he Lock-In saus. The innovaion A is diffused in he clusers. Diffusion didn cover all he nework. Tha is why A is in sauraion earlier han B. A firs he Innovaion Perceive is small and B s diffusion poins are less han A s, which made B has less possibiliy o ge ino he saus Lock-In and diffuse o he whole nework. Bu he increase of Innovaion Perceive produces he difference of he level of wo innovaions. And according o he analysis above, he increase of W 1 can avoid he Lock-In saus effecively. Tha is why A s marke share is bigger han s. When W 1 = 0.27, here are abou 500 nodes adop A and here are abou 300 nodes adop B. Then we increase W 1 again, he number of nodes added for boh A and B is less. When W 1 = 0.29, he siuaion is a lile beer han W 1 = Tha is means he effec of he increase of Innovaion Perceive is decrease while he increase of Innovaion Perceive. And a ha momen, he compeiion mechanism influences he diffusion more The Sensiive Analysis of W 3 Firs we simulae he oally diffusion. We se he parameer like W 1A = 0.3; W 1B = 0.3; W 2A = 0.7; W 2B = 0.7; W 3A = 0.1; W 3B = 0.1; W 4A =0.2; W 4B = 0.2; R = 0.5; L = Under his condiion, he marke share of A is 631 while he marke share for B is 349. Tha is because he A s diffusion poins is more han B s (A s iniial marke share is higher han B s). Then we adus he B s word of mouh W 3B, o check how word of mouh influences he diffusion. By he increase of he value of B s word of mouh coninuously, we ge he resul which is demonsraed in he Figure 3. Wih he increase of s word of mouh, from 0.1 o 0.7, innovaion s marke share is upping. We can see how i cach up wih A and finally exceed A. The deailed diffusion imes and boos sep of he value of word of mouh is in Figure 3. From he Figure 3 we can find ha he increase of word of mouh of B has lile impac on diffusion. Jus decrease some diffusion imes. Bu i has he disinc boos on s marke share. The way o increase he word of mouh in he real world can hrough he beer package, he beer service. of adopers W1(A)=W1(B)=0.25, W = W 1(B) = 0.25, A A W1(A)=W1(B)=0.25, W = W 1(B) = 0.25, B B W1(A)=W1(B)=0.27, W = W 1(B) = 0.27, A A W1(A)=W1(B)=0.27, W = W 1(B) = 0.27, B B W1(A)=W1(B)=0.29, W = W 1(B) = 0.29, A A W1(A)=W1(B)=0.29, W = W 1(B) = 0.29, B B Simulaion ime Figure 2. Influence of W 1.. of adopers W3(B)=0.1,W3(A)=0.1, W 3(B) = W 3(A) = 0.1, A A W3(B)=0.1,W3(A)=0.1, W 3(B) = W 3(A) = 0.1, B B W3(B)=0.25,W3(A)=0.1, W 3(B) = W 3(A) = 0.1, A A W3(B)=0.25,W3(A)=0.1, W = W 3(A) = 0.1, B B W3(B)=0.5,W3(A)=0.1, W = W 3(A) = 0.1, A A W3(B)=0.5,W3(A)=0.1, W = W 3(A) = 0.1, B B Simulaion ime Figure 3. Influence of W 3B.

5 202 Y. F. YAN, Y. LI Figure 4. Influence of W 4B. or he cusomized design o make i. The simulaion above is o demonsrae ha if one wih lower iniial marke share wans o cach up wih he one wih higher iniial marke share, i needs o increase is word of mouh The Sensiive Analysis of W 4 Nex we will adus s W 4B which is he adverisemen parameer o see how i influences he diffusion of innovaion B. By he increasing s adverisemen coninuously, we ge he resul shown in Figure 4. From Figure 4 we can find ha he increase of adverisemen will enlarge s marke share. When W 4B increases from 0.2 o 0.45, s marke share increases from 350 o 900. There are wo special characers for he increase of adverisemen according he figure above. 4. Conclusions According o he simulaion, we find ha he middle sage is he ime when o enlarge he marke share. The one wih higher iniial marke share is easier o ge ino he Lock-In saus, which can be escaped by increasing he Innovaion Perceive. In he real marke, if here are wo innovaions and one is wih higher marke share comparing wih he oher, he governmen can decrease he marke gap by increasing he enrance hreshold which can be achieved by launching some policies or publishing some guides. For he one wih higher marke share, i can increase he nodes Accepance Trend which can be achieved by publishing he innovaion informaion o increase is marke share and decrease he lower one s marke share. Acually, he model proposed in his paper is sill a simple one, wih only one kind of agen. Also, he cos of acceping a new echnology or produc is ignored. And i will be beer if he empirical sudy will be operaed o adus he parameer of he model. REFERENCES [1] E. M. Rogers and M. Evere, Diffusion of Innovaions, 4h Ediion, The Free Press, New York, [2] L. Riccardo, Segmenaion and Increasing Reurns in he Evoluionary Dynamics of Compeing Techniques, Meroeconomica, Vol. 52,. 2, 2001, p. 2. [3] C. Waanabe, Reiko Kondo: A Subsiuion Orbi Model of Compeiive Innovaions, Technological Forecasing & Social Change, Vol. 71,. 4, 2004, pp doi: /s (02) [4] B. Zhang, L. Fang and R. B. Zhang, A Dynamic Diffusion Model of Compeiive Muli-Innovaions and Is Applacaion, Technology Economics, Vol. 27,. 9, 2008, pp. 5-9, 19. [5] R. Nie, K. M. Qian and D. H. Pan, The Innovaive Technology Diffuse Models and Their Sabiliy Analysis Base on Logisic Equaion, Journal of Indusrial Engineering and Engineering Managemen, Vol. 20,. 1, 2006, pp [6] Y. H. Liu and J. R. Dong, Innovaion Produce and Technology Comparaive Diffusion, Journal of Indusrial Technological Economics, Vol. 25,. 7, 2006, pp [7] F. M. Bass, A New Produc Growh Model for Consumer Durables, Managemen Science, Vol. 15,. 5, 1969, pp doi: /mnsc [8] D. J. Was and S. H. Srogaz, Collecive Dynamics of Small-World Neworks, Naure, Vol. 393,. 6684, 1998, pp doi: /30918 [9] D. Maienhofer, Finding Opimal Targes for Change Agens: A Compuer Simulaion of Innovaion Diffusion, Compuaional & Mahemaical Organizaion Theory, Vol. 8,. 4, 2002, pp doi: /a: