An Analysis on Stability of Competitive Contractual Strategic Alliance Based on the Modified Lotka-Voterra Model

Transcription

1 Advanced Scence and Technology Letters, pp An Analyss on Stablty of Compettve Contractual Strategc Allance Based on the Modfed Lotka-Voterra Model Qng Xueme 1, Zhang Weguo 1,2 1 School of Economcs and Busness Admnstraton, Chongqng Unversty, Chongqng , Chna 2 College of Economcs and Management, Southwest Unversty, Chongqng , Chna qngxuemelx@126.com, wgzhang@cqu.edu.cn Abstract: Orgnal competton, nter-allance competton and cooperaton consttute all together co-opetton relatons n compettve contractual strategc allance, whch dctate the stablty of the allance by means of affectng the profts of allance partners. A modfed Lotka-Voterra model s establshed usng system dynamcs, due to the smlarty of enterprses and allances to bologcal systems. Accordng to the analyss of modfed Lotka-Voterra model, we fnd: there exsts stable boundary n allance, the extent of co-opetton wthn an allance determnes ts drecton,.e. dfferences n the extenson of co-opetton result n the dfferences of allance revoluton; Co-opetton between allance partners s not always the same, but changng constantly. The system evaluates wth ts co-opetton changng; Penalty costs and allance cycle affect the stablty of Compettve strategc allance besdes co-opetton. Keywords: Co-opetton, compettve contractual strategc allance, stablty, system dynamcs, Lotka-Voterra model 1. Introducton Compettve contractual strategc allance embodes two entrely dfferent logc prncples that contradct each other [1-2], whch causes nstablty of compettve contractual strategc allance. Usually, nstablty of such allance means short and fragle cooperaton, and the falure of allance [3]. However, there are few studes done to examne the stablty of compettve contractual strategc allance. The exstng ones stll ddn t analyze the dynamcs and systematcs of allance stablty. To make for the defcences of exstng studes, ths paper constructed system cycle dagram usng system dynamcs, and developed the ISSN: ASTL Copyrght 2014 SERSC

2 Advanced Scence and Technology Letters dynamcs equaton,.e. Lotka Voterra model, for compettve strategc allance based on contract by applyng modfed logstc model, so as to dscuss the nfluence of co-opetton on such allance. 2. Modfed Lotka-Voterra Model Compettve contractual strategc allance s an open and complcated system. Allance system s cycle dagram s shown n Fg.1. Market smlarty and contractual control dscrmnate compettve contractual strategc allance from other types of allances. Market smlarty dctates that allance partners are no more than compettors to each other. Contractual control s not only ncapable of elmnatng competton from partners, but also generates dervatons, such as learnng competton and barganng. The former s referred to as orgnal competton, whereas the latter s called nter-allance competton. The allance s performance s affected by co-opetton, and dctates the stablty of an allance. Accordngly, the stablty mechansm of compettve contractual strategc allance s shown n Fg.2. allance goal allance control Gap between goal and performance - allance performanc e co-opetton Fg. 1. system cycle dagram of compettve contractual strategc allance Copyrght 2014 SERSC 61

3 Advanced Scence and Technology Letters market smlarty orgnal competton contractual control nter-allance competton co-opetton partner s proft allance stablty orgnal competton Fg. 2. the Stablty Mechansm of Compettve contractual strategc allance 1 Correspondng ntensty of co-opetton s defned as follows: Partner s ntensty of co-opetton c j : co-opetton s degree of nfluence on allance partner,the varaton of partner s proft growth rate caused by partner j s dr ' proft change,.e.: cj ( ) com0 com coo R dt j In the equaton, R s the proft of partner, com0 s the ntensty of orgnal ' competton, whereas com s the allance partner s ntensty of nter-allance competton; coo s the allance partner s ntensty of cooperaton; ' ( com coo ) s the nter-allance co-opetton effect, namely the allance effect,, j 1,2, j. Notably, the symbol means mergng, not addng. In ecology perspectve, enterprses are ntellgent lvng organsm wth vtal sgns [4-5]. Accordng to ecologcal theores, under the condton of partner s ndvdual exstence, growth rate of partners proft follows classcal logstc model, whereas allance s growth rate follows Lotka-Voterra model [6], thus: dr R Rb (1 ) (1) dt N In the equaton, b denotes partner s nternal growth rate, namely the enterprse s growth rate decded by partner s own nternal characterstcs, and usually b 0. N denotes the maxmum proft partner can acqure wthout the varatons of tme, locaton and resource. In equaton (1), when b 0 and R N (allance s proft surpasses ts lmt), calculaton results n a unreasonable outcome,.e. dr 0. Therefore, classcal dt logstc model has been modfed by T.G.Hallam and C.E.Clark as follows: 1 Allance n the Fgure s referrng to specfcally the Compettve contractual strategc allance. 62 Copyrght 2014 SERSC

4 Advanced Scence and Technology Letters dr R ( b cr ) ( 1,2 ) (2) dt In equaton (2), c denotes the restrcton of necessary nvestments for partner s proft growth factors, and c 0. R () t Defnton: u denotes partner s actual market share at tme t. N Obvously, R s postvely correlated to u, and n case of partner s ndvdual exstence, 0 u 1; before allance, 0 u 1; after, u 0.Then: du1 b1u 1(1 u1 1u2 ) dt du2 b2u2 (1 u2 2u1) dt (3) Ths s the modfed Lotka Voterra model based on modfed logstc. 3. Model Analyss 3.1 Equlbrum There are four equlbrums n model (4): P 1 (0,0), P 2 (0,1), P 3 (1,0) and 1 1 (, ) 1 2 P Accordng to theory of stablty, equlbrum pont P 1 s unstable under any crcumstances;equlbrum P 2 gradually stablzes when 1 1 ; equlbrum pont P 3 gradually stablzes when 2 1 ; equlbrum pont P4 stablzes gradually when and Stablty Boundares Postve equlbrum pont P4 approaches stablty gradually, ndcatng that compettve contractual strategc allance s stable. From the stablty condtons of equlbrum pont P 4, the allance s table when the degree of allance partner s co-opetton s located n the range of and 1 2 1, meanng n ths range, although the degree of allance partners co-opetton s possbly changed for adaptaton, but the allance remans stable and the system has resstance and recoverablty. Outsde of ths range, the allance s stablty s breached and the allance cannot contnue. Accordngly, the stablty boundares of compettve contractual strategc allance s obtaned and shown n Fg.3. Copyrght 2014 SERSC 63

5 Advanced Scence and Technology Letters Fg. 3. The Stablty Boundares of Compettve contractual strategc allance 4. Further Dscusson of the Model Compettve contractual strategc allance has three dfferent outcomes, ncludng dsntegraton, mergng and co-exstence (passve co-exstence and stable co-exstence), whch correspond to equlbrum ponts P 2 P 3 and P 4. Allance s operaton, control and the realzaton of ts target s tme consumng. As a result, the actual outcome of allance evoluton s affected by not only the degree of allance partner s co-opetton, but also allance cycle and penalty cost. The stablty of compettve contractual strategc allance s a systematc characterstc manfested under the nfluence of a seres of factors that can be put nto competton and cooperaton [19] carryng on smultaneously,.e. co-opetton. After the establshment of allance, co-opetton between allance partners s not always be the same, but changng constantly. The contnuous moton of co-opetton s the mpetus of allance system s evoluton, whch place the system n dfferent state of stablty. 5. Concluson Orgnal competton, nter-allance competton and cooperaton consttute all together co-opetton relatons n compettve contractual strategc allance. Co-opetton nfluences allance partners by means of affectng ther proft, so as to decde the stablty of compettve contractual strategc allance. Under the condton of partner s ndvdual exstence, ts growth rate follows modfed classcal logstc 64 Copyrght 2014 SERSC

6 Advanced Scence and Technology Letters model, whereas allance s growth rate follows Lotka Voterra model.through analyzng the modfed Lotka Voterra model, t s found: (1)The dfferences of co-opetton degree result n dfferent outcomes of allance system s evoluton. There exsts stable boundary. (2) Co-opetton between allance partners s not always the same, but changng constantly. (3) Penalty costs and allance cycle affect the stablty of Compettve strategc allance besdes co-opetton, whch should be pad more attenton. Acknowledgements: Ths work was supported by Grants from MOE (Mnstry of Educaton n Chna) Project of doctoral secton (no ) References 1. Hll CC., L H., Daves B, The paradox of cooperaton and competton n strategc allances: Towards a mult-paradgm approach, Management Research News, vol. 26, no. 1, (2003), pp Zneldn M, Co-opetton the organzaton of the future, Marketng Intellgence & Plannng, vol. 22, no. 6/7, pp Kun Zhang, Study on Strategc Allance Instablty Base on Game Theory, Shanx Unversty (2010) 4. Zhongzh Yang, Introducton to Enterprse Ecology, Scence Press, Bejng, (2003) 5. Yuan Lou, Hong Zhao, The Model of Enterprses Ecosystem and the Analyss of Abotc Envronment Factors, The Journal of Quanttatve & Techncal Economcs, no. 3, (2002), pp Lnzhou Lu, Bo Wu, Wenxa Sun, On the Stablty of Strategc Allance of Technologcal Innovaton: Development Model Study, Scence & Technology Progress and Polcy, no. 3, (2012), pp Copyrght 2014 SERSC 65