Co-opetition and the Stability of Competitive Contractual Strategic Alliance: Thinking Based on the Modified Lotka-Voterra Model

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1 Internatonal Journal of u- and e- Servce, Scence and Technology Vol.8, No. (05), pp Co-opetton and the Stablty of Compettve Contractual Strategc Allance: Thnkng Based on the Modfed Lotka-Voterra Model Xueme Qng and Weguo Zhang, School of Economcs and Busness Admnstraton, Chongqng Unversty, Chongqng , Chna College of Economcs and Management, Southwest Unversty, Chongqng 40075, Chna Abstract Co-opetton s the key feature of compettve contractual strategc allances. Orgnal competton, nter-allance competton and cooperaton consttute all together co-opetton relatons n compettve contractual strategc allance. Such relatons 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. Introducton Compettve contractual strategc allance embodes two entrely dfferent logc prncples that contradct each other [-], whch causes nstablty of compettve contractual strategc allance. Usually, nstablty of such allance means short and fragle cooperaton, and the falure of allance [3]. Accordngly, to make the most of compettve contractual strategc allance n global competton, the ssue of nstablty has to be solved. However, there are few studes done to examne the stablty of compettve contractual strategc allance. The exstng ones manly focused on two aspects. One s the movement of two contradctng forces, competton and cooperaton, and ther nfluence on the stablty of allance,such as Das and Teng s [4] and Feqong Chen and Langcong Fan [5]. Such studes haven t taken enough nto account the systematcs and dynamcs of allances stablty. The other s based on the smlarty of enterprses to lvng organsms [6], regardng allances as eco-systems. Also, ecologcal theores and models were appled n ther study to analyze the nfluence of co-opetton on strategc allance s stablty, such as Yongmng Sheng, Weguo Zhang and Xueme Qng [7]. In Lterature [8-4], classcal logstc model and Lotka-Voterra model based on classcal logstc model were appled to analyze the nfluence of co-opetton on strategc organzatons (ncludng strategc allances and networks) stablty. These studes ISSN: IJUNESST Copyrght c 05 SERSC

2 Internatonal Journal of u- and e- Servce, Scence and Technology Vol.8, No. (05) stll ddn t analyze allance system s dynamc operaton process. Besdes, classcal logstc model was appled to the crcumstances of enterprse s growth surpassng ts lmt. To make for the defcences of exstng studes, ths paper constructed system cycle dagram usng system dynamcs, and developed the dynamcs equaton,.e., L o tka V o terra 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.. Stablty Mechansms of Compettve Contractual Strategc Allance: the Constructon of Modfed Lotka-Voterra Model.. The System of Compettve Contractual Strategc Allance From the perspectve of system theory, a system s the ntegraton of nterrelated and nteractng elements, and all thngs n real world exst and operate by means of system. Compettve contractual strategc allance s an open and complcated system. Wth the establshment and operaton of allance, ts target and performance come nto play. The operaton and control of allance need to be contnuously evaluated n term of performance, and compared wth ts target. Gaps between target and performance requre correspondng allance control and management. Allance system s cycle dagram s shown n Fgure... The Stablty Mechansms of Compettve Contractual Strategc Allance Compettve contractual strategc allance s nsttuton arrangement. At the same tme, t s also an ecologcal system, the stablty of whch features both system balance and ecologcal stablty. The ultmate goal of any allance, whatever motves t mght have, s to acqure approprate fnancal return. Proft that has been or wll be obtaned s gong to affect allance partners current and next co-opetton decson, and t s also dctates strategc optons, such as jonng an allance or not, the tme to jon and stayng n the allance or not. An allance s performance s the decdng factor of ts stablty [5]. 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. Both types of compettons exst n an allance, always and everywhere, affectng each other and cooperaton between partners. The three of them are recprocal to each other, mutually beneftng, ntegratng and formng nto the co-opetton n compettve contractual strategc allance. And 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 Fgure. 68 Copyrght c 05 SERSC

3 Internatonal Journal of u- and e- Servce, Scence and Technology Vol.8, No. (05) allance goal + allance control + Gap between goal and performance - allance performanc e + co-opetton + Fgure. System Cycle Dagram of Compettve Contractual Strategc Allance market smlarty orgnal competton contractual control nter-allance competton co-opetton partner s proft allance stablty orgnal competton Fgure. The Stablty Mechansm of Compettve Contractual Strategc Allance Allance n the Fgure s referrng to specfcally the Compettve contractual strategc allance. Copyrght c 05 SERSC 69

4 Internatonal Journal of u- and e- Servce, Scence and Technology Vol.8, No. (05).. Constructng Lotka-Voterra Model for Compettve Contractual Strategc Allance... Co-opetton Defnton: 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 proft change,.e.,: dr dt c dr ( ) c o m ' c o m c o o R d t j 0 j In the equaton, R s the proft of partner, a contnuously dfferentable functon of tme t ; s the proft growth rate of partner ; c o m 0 s the ntensty of orgnal competton, ' whereas com s the allance partner s ntensty of nter-allance competton; c o o s the ' allance partner s ntensty of cooperaton; ( co m co o ) s the nter-allance co-opetton effect, namely the allance effect,, j,, j. Notably, the symbol + means mergng, not addng.... Lotka-Voterra Model for Compettve Contractual Strategc Allance: In ecology perspectve, enterprses are ntellgent lvng organsm wth vtal sgns [6-7]. As for contractual allance bult by two competng enterprses, co-opetton between partners s smlar to the nteracton between botc groups, whch consttute de facto an eco-system. 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 [8], thus: d R d t R Rb( ) N () In the equaton, t denotes tme, snce factors affectng proft level can be deemed as functons of tme, such as technology, nformaton, professonalsm, dvson of labor, nvestment and transacton cost. As a result, tme t not only ncludes ts everyday meanng, but also all the varatons that are nfluencng enterprses proft level. 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 (), when b 0 and R N (allance s proft surpasses ts lmt), calculaton dr results n a unreasonable outcome,.e. 0. Therefore, classcal logstc model has been modfed by T. G. Hallam and C. E. Clark as follows: dr R ( b c R ) (, dt dt ) () In equaton (), c denotes the restrcton of necessary nvestments for partner s proft growth factors, such as resources and envronment, reflectng the enterprse s own retardant growth effect, and c 0. Before allance, the two partners are only compettors. However, they are competng and cooperatng at the same tme. Besdes affectng co-opetton between partners, contractual control dctates that the number of subject wthn an allance s same as that of partners. Then, To facltate dscusson, the number of allance partners s lmted to. 70 Copyrght c 05 SERSC

5 Internatonal Journal of u- and e- Servce, Scence and Technology Vol.8, No. (05) the partners proft n a compettve contractual strategc allance follows modfed L o tka V o terra model: dr R ( b c R c R ) dt dr R ( b c R c R ) dt (3) Defnton: u R ( t) denotes partner s actual market share at tme t. Obvously, R N postvely correlated to u, and n case of partner s ndvdual exstence, 0 u ; before allance, 0 u ; after, u 0. N N, c c,, N N Let c c,then model (3) becomes: s du dt du b u ( u u ) b u u u dt Ths s the modfed L otka postvely correlated to c j value of ( ) V oterra model based on modfed logstc. Obvously, s,and capable of reflectng partner s degree of co-opetton. The denotes the nfluence of allance partner j s market share fluctuatons has on allance partner s make share growth rate( j). (4) 3. Model Analyss 3.. Equlbrum There are four equlbrums n model (4): P (0, 0 ), P (0,), P 3 (, 0) and P4 (, ) Snce equlbrums are the system s fx ponts, representng the ultmate state of systematc development. In terms of compettve allance systems based on contracts, the ultmate state of proft must be a non-negatve value. As a result, only when P 4 s a postve equlbrum pont, the model makes sense. Accordng to the theory of stablty, equlbrum pont P s unstable under any crcumstances;equlbrum pont P gradually stablzes when ;equlbrum pont P 3 gradually stablzes when ;equlbrum pont P stablzes gradually when 4 and,as ndcated n Table.. Copyrght c 05 SERSC 7

6 Internatonal Journal of u- and e- Servce, Scence and Technology Vol.8, No. (05) Table. Stablty Condtons of All Equlbrum Ponts Equlbrum Pont Stablty Condton Stablty P Unstable under any condtons Unstable P Gradually stable P 3 Gradually stable P 4 Gradually stable 3.. Co-opetton and the Stablty of Allance System In terms of compettve contractual strategc allance, there are three possble outcomes, ncludng dsntegraton, merger and stablzaton. For each equlbrum: P and P 3 represent that one allance partner merged another. For equlbrum P and P 3, f allance lasts long enough, one of the partners wll be merged; and the allance wll dsntegrate f otherwse. Postve equlbrum pont P represents that all allance partners has acqured maxmum 4 fnancal return under exstng condtons. It proves allance partners proft s hgher than before wth only compettons, and the partners are lack of motvaton to leave: the allance remans stable. Orgnal competton s decded by the busness scope and wll not dsappear wth establshment of allance: c o m 0 s true all the way through allance. Inter-allance 0 competton and cooperaton consttute all together nter-allance co-opetton. For allance to sustan, nter-allance co-opetton effect,.e. allance effect must stay postve, thus c o m 0, c o o 0, and c o m c o o 0. Accordngly, n terms of compettve strategc allance system based on contract, allance partner s co-opetton s possbly both postve and negatve. By examnng the stablty of all equlbrum ponts, t s found that the degrees of co-opetton are located n dfferent range and the states of stablty on each pont are dfferent from each other, thus the evoluton outcomes of compettve contractual strategc allance vares, whch s shown n Fgure Stablty Boundares Postve equlbrum pont P approaches stablty gradually, ndcatng that compettve 4 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 7 Copyrght c 05 SERSC

7 Internatonal Journal of u- and e- Servce, Scence and Technology Vol.8, No. (05) of and, 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 Fgure 4. Fgure 3. Allance System Evoluton wth Dfferent Co-opetton Copyrght c 05 SERSC 73

8 Internatonal Journal of u- and e- Servce, Scence and Technology Vol.8, No. (05) - - Fgure 4. The Stablty Boundares of Compettve Contractual Strategc Allance 4. Further Dscusson of the Model 4.. Co-opetton, Penalty cost, Allance Cycle and Stablty 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 P 3 and P 4. Allance s 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. If the allance s penalty cost s too hgh, the ext standards wll be rased accordngly. From the stablty condtons of all equlbrum ponts, as long as the degree of co-opetton s too low for one of the allance partners, competton effect s far more ntense than co-opetton effect,.e. the degree of co-opetton (, ) { (, ) } { (, ) }. If penalty cost s too hgh and allance cycle s long enough, the passve co-exstence of allance partner (s) wll evolve nto mergng. However, f penalty cost s too low, no matter how long the cycle s, the allance wll end up wth dsntegraton. 4.. Co-opetton Evoluton and the Stablty of Compettve Contractual Strategc Allance 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 [9] carryng on smultaneously,.e. co-opetton. After the establshment of allance, co-opetton between allance partners s not always be the same, but changng 74 Copyrght c 05 SERSC

9 Internatonal Journal of u- and e- Servce, Scence and Technology Vol.8, No. (05) constantly. The contnuous moton of co-opetton s the mpetus of allance system s evoluton, whch place the system n dfferent state of stablty. * * Assume that the equlbrum pont of model (4) s ( u, u ), snce when 0, the allance s stablty boundary s not a straght lne but hyperbola. To facltate dscusson, t s assumed that (dscusson remans the same when vares). Then, the change of allance partner s equlbrum pont s shown n equaton (5) and Fgure 5: u * (5) Out of the same consderaton, s an assumed value for the dscusson of allance partner s equlbrum state changng wth co-opetton evoluton. Then, the actual market share equlbrum soluton of allance partner s shown n equaton (6) and Fgure 6: u * (6) * u * u Fg.5 The Dagram of Allance Partner s Equlbrum Evoluton wth Co-opetton Fg.6 The Dagram of Allance Partner s Equlbrum Evoluton wth Co-opetton From equaton (5), (6) and Fgure (5), (6), t s obvous that the partners equlbrum profts vares wth ts co-opetton changng. Copyrght c 05 SERSC 75

10 Internatonal Journal of u- and e- Servce, Scence and Technology Vol.8, No. (05) 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 model, whereas allance s growth rate follows L otka V oterra model. Through analyzng the modfed L o tka V o terra model, t s found: ()The dfferences of co-opetton degree result n dfferent outcomes of allance system s evoluton. A stable state s achevable when 0, 0, ; Ether over competton(e. ) or over cooperaton (e. 0, ) s adverse for the stablty of allance system. Then the stable boundary exsts. () Co-opetton between allance partners s not always the same, but changng constantly. The contnuous moton of co-opetton places the allance n dfferent state of stablty, such as dsntegraton, mergng and stablty. (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 [] C. C. Hll, H. L and B. Daves, The paradox of cooperaton and competton n strategc allances: Towards a mult-paradgm approach, Management Research News, vol. 6, no., (003), pp. -0. [] M. Zneldn, Co-opetton the organzaton of the future, Marketng Intellgence & Plannng, vol., no. 6-7, pp [3] K. Zhang, Study on Strategc Allance Instablty Base on Game Theory, Shanx Unversty, (00). [4] T. K. Das and B. S. Teng, Instabltes of strategc allances: an nternal tensons perspectve, Organzaton Scence, vol., no., (000), pp [5] F. Q. Chen and L. C. Fan, Stablty Analyss of Strategc Allances Based on Cooperaton and Competton, Management World, no. 7, (007), pp [6] P. N. Ruan, J. W. Zhang and Y. L, Study of Prcple and Mannagement of Relaton among Nodes n Strategc Networks, Scence of Scence and Management of S.& T, vol. 9, no. 4, (008), pp [7] Y. M. Sheng, W. G. Zhang and X. M. Qng, Study on the Stablty of Co-opettve Strategc Allance, Statstcs and Decson, no. 0, (009), pp [8] M. X. Wang, Research on the Evoluton Mechansm about Compettve Strategc Allance System of Enterprse, Yanshan Unversty, (00). [9] C. Y. Gao and P. Du, The Cooperaton and Competton Model of Inter-members n Hgh-tech Vrtual Industral Cluster Based on Lotka-Volterra, Scence & Technology Progress and Polcy, no., (009), pp [0] B. Han and Q Meng, Analyss on System Structure Evoluton for the Formng of Strategc Allance Synergy Mechansm, Scence & Technology Progress and Polcy, no., (007), pp [] Y. Y. Wu and P. C. Mang, Study on the Stablty of Strategc Networks Based on Enterprse Ecology, Scence & Technology Progress and Polcy, no. 6, (00), pp [] X. Z. Zhuo, X. Wang and Z. F. Wang, A Study on the Coopetton Relatonshp among Alled Partners of Supply Chan Enterprses Based on the Volterra Model, Journal of Industral Engneerng and Engneerng Management, vol. 4, no., (00), pp Copyrght c 05 SERSC

11 Internatonal Journal of u- and e- Servce, Scence and Technology Vol.8, No. (05) [3] H. X. Ye, P. Z. Zhang and J. Sun, Dynamc Cooperaton-competton n Interest-group, Journal of Industral Engneerng and Engneerng Management, vol. 6, no., (00), pp [4] Y. Yan and M. Q. L, Dynamc Analyss of Network Organzatons Evoluton Based on Co-opetton Relaton, Systems Engneerng, vol. 7, no. 0, (009), pp [5] X. Ren and Z. P. Zhang, Mechansm of Strategc Allance Evoluton Based on Allance Performance, Internatonal Conference on Engneerng and Busness Management, (0), pp [6] Z. Z. Yang, Introducton to Enterprse Ecology, Scence Press, Bejng, (003). [7] Y. Lou and H. Zhao, The Model of Enterprses Ecosystem and the Analyss of Abotc Envronment Factors, The Journal of Quanttatve & Techncal Economcs, no. 3, (00), pp [8] L. Z. Lu, B. Wu and W. X. Sun, On the Stablty of Strategc Allance of Technologcal Innovaton: Development Model Study, Scence & Technology Progress and Polcy, no. 3, (0), pp [9] J. R. Ca, Partner Characterstcs, Credble Commtment and the Stablty of Strategc Allances, Scence of Scence and Management of S. & T, no. 7, (0), pp Authors Xueme Qng, she s a doctoral canddate n the school of Economcs and Busness Admnstraton, Chongqng Unversty, Chna. Her research nterests nclude strategc management and Econometrcs. Weguo Zhang, he s a Professor n the School of Economcs and Management, Chongqng Unversty, Chna. Hs research nterests are n the felds of strategc management, knowledge management and fnancal management. Copyrght c 05 SERSC 77

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