# Yi Zhao, 1 Dong Li, 1 and Liqiang Pan Introduction and Literature Review

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3 Discrete Dynamics in Nature and Society 3 design method [20]. Yang et al. (2014) built up a new dynamic Cournot duopoly game model with team players in exploitation of a renewable resource [21]. However, the existing literature has little research on the relationship between Chinese big data-based e-commerce financial institutions and commercial banks, less application of mathematical logic methodologies [22, 23]. The coopetition relationship between Chinese e-commerce financial institutionsandcommercialbankswouldbeanalyzedin detail from the prospective of evolutionary game in the paper. 2. The Fundamental Hypothesis (H1) Let I={1,2}represent the two bounded rational players in the game, respectively, that is, a commercial bank and big data-based e-commerce financial institutions. Moreover, let S1 = S2 = {competition, cooperation} be the strategic set of each participant. That is to say, there are two strategies for each player to choose. Cost needs to be paid when the two players cooperate, while the cost is 0 on the contrary. (H2) When the two players choose cooperation, both of them provide a part of resource of their own and share the benefits from transaction to each other. When both of them choose competition, neither would like to cooperate with each other, indicating that each one provides client-oriented financial services, pays transaction costs, and earns net income alone. If one player chooses cooperation and gives his own resource to the other, the other one chooses competition and then could complete the transaction alone without paying any cost. The net income is uncertain for each player who provides resource. Therefore, the cost of cooperation is definitely not less than they should spend in cooperation of two sides. Meanwhile, player who gets the resource will attain all the income of the transaction and the transaction costs should be considered as 0. (H3) When both the commercial bank and the e- commerce financial institution choose cooperation together, αa (α 1, A 0)andC 1 are the income and cost of the commercialbank,respectively,andthenthenetincomeofthe commercial bank should be αa C 1.Similarly,βB (β 1, B 0)andC 2 are the income and cost of the e-commerce financial institution, respectively, and then the net income of the e-commerce financial institution should be βb C 2. α (α 1)andβ (β 1) which means the degree of the cooperation are, respectively, known as the cooperation coefficients for two sides. (H4) When the commercial bank and the e-commerce financial institution both choose competition, A 1 and B 1 (A 1,B 1 0) are the income of the commercial bank and the e-commerce financial institution, respectively. (H5) When the commercial bank prefers cooperation while the e-commerce financial institution prefers competition, A C 1 (C 1 C 1 0)andB are the net income of the commercial bank and the e-commerce financial institution, respectively. On the contrary, when the commercial bank prefers competition while the e-commerce financial institution prefers cooperation, A and B C 2 (C 2 C 2 0)are Table 2: Coopetition game payoffs matrix. Commercial E-commerce financial institution bank Cooperation Competition Cooperation αa C 1, βb C 2 A C 1, B Competition A, B C 2 A 1, B 1 the net income of the commercial bank and the e-commerce financial institution, respectively. (H6) p (0 p 1) is the probability for the commercial bank which chooses cooperation, and then 1 pis the probability for competition. q (0 q 1) is the probability for the e-commerce financial institution which chooses cooperation, and then 1 qis the probability for competition. On the basis of mentioned hypothesis above, the payoffs matrix is in Table Model and Analysis Basedonpayoffsmatrixabove,thecommercialbankmay choose cooperative or competitive strategy, as shown below: E(U 1 ) p =q(αa C 1 )+(1 q)(a C 1 ), E(U 1 ) 1 p =qa+(1 q)a 1. Average payoffs of the mixed strategy chosen by the bank are shown blow: (1) E(U 1 )=pe(u 1 ) p +(1 p)e(u 1 ) 1 p. (2) If the expected payoffs of a particular strategy are more than the average payoffs of the mixed strategy, this strategy will tend to be replicated. According to the replicator dynamics of evolution games, assume that the relative adjustment speed of itsdynamicschangewhichcanberepresentedbydifferential equation is proportional to the range of payoffs that is more than the average payoffs. The replicator dynamics equation including independent variables is shown below: dp dt =p[e(u 1) p E(U 1 )]. (3) Similarly, the big data-based e-commerce financial institution chooses cooperative and competitive strategy, respectively, as shown below: E(U 2 ) q =p(βb C 2 )+(1 p)(b C 2 ), (4) E(U 2 ) 1 q =pb+(1 p)b 1. (5) Average payoffs of the mixed strategy chosen by the big databased e-commerce financial institution are shown below: E (U 2 ) =qe(u 2 ) q + (1 q) E (U 2 ) 1 q. (6) Similarly,itcanbeconcludedthatreplicatordynamicsequation including independent variables is shown below: dq dt =q[e(u 2) q E(U 2 )]. (7)

4 4 Discrete Dynamics in Nature and Society Table 3: Stability test calculations of local equilibrium solutions. Local equilibrium solutions DetJ TrJ O(0, 0) (A A 1 C 1 )(B B 1 C 2 ) A A 1 C 1 +B B 1 C 2 A(0, 1) ( A + αa C 1 )( B + B 1 +C 2 ) A+αA C 1 B+B 1 +C 2 B(1, 0) ( A + A 1 +C 1 )( B + βb C 2) A+A 1 +C 1 B+βB C 2 C(1, 1) (A αa + C 1 )(B βb + C 2 ) A αa+c 1 +B βb+c 2 D point X 0 Let dp dt =p[e(u 1) p E(U 1 )] = 0, dq dt =q[e(u 2) q E(U 2 )] = 0. Consequently, five local equilibrium solutions (p, q) can be calculated by Mathematica 9.0, as shown in Table 3: O: (0, 0), A: (0, 1), B: (1, 0), C: (1, 1), D: (( B + B 1 +C 2 )/( 2B + βb + B 1 C 2 +C 2 ), ( A + A 1 +C 1 )/( 2A + αa + A 1 C 1 +C 1 )). BasedonmethodofferedbyFriedman[24], the evolutionary stability of the whole game can be concluded by calculating Jacobi determinant of replicator dynamics equation (8). LetJ represent Jacobi matrix of (8); thenits determinant and trace are DetJ and Tr J. DetJ > 0 and Tr J<0 the local equilibrium solutions (p, q) is ESS; if (p, q),detj<0 (p, q) is saddle point: X= (A(α 1) +A 1 C 1 +C 1 )(A(α 1) C 1) ( A + A 1 +C 1 )(B(β 1) C 2)( B+B 1 +C 2 ) (((α 2) A+A 1 C 1 +C 1 )2 (B (β 2) + B 1 +C 2 C 2)) 1. On the basis of Friedman method [24], as the local equilibrium solutions stability test result shows, the evolutionary stability can be analyzed to conclude an ESS justification under different circumstances, as detailed below. (1) Consider A A 1 C 1 <0and B B 1 C 2 <0 DetJ >0and Tr J < 0 (0, 0) is the ESS. Namely, A C 1 < A 1 and B C 2 < B 1 (0, 0) is theess.obviously,basedontable2,theevolutionarystable strategy is that both of them choose competition together. This situation usually occurs before establishment of the e- commerce financial institution which needs to improve in such aspects as capital strength, professional financial ability, securities, and credit conditions. It is premature to cooperate with commercial banks for one e-commerce corporation, due to its lack of advanced financial professionals and not having formed a brand effect. According to credit investigation system of People s Bank for loan business, commercial banks would ignore the e-commerce financial institution s big databasedcustomercreditevaluationsystemandwouldnothave the sense of cooperation. According to hypothesis (H2), the net income of cooperation chosen by the e-commerce (8) (9) financial institution is less than that of noncooperation. Therefore, (competition, competition) serves as the evolutionary stable strategy (ESS) in this period. (2) Consider A + αa C 1 <0and B + B 1 +C 2 <0 DetJ >0and Tr J < 0 (0, 1) is the ESS. Namely, αa C 1 <Aand B 1 <B C 2 (0, 1) is the ESS. Obviously,basedonTable2, the evolutionary stable strategy is that the commercial bank chooses competition and the e-commerce financial institution chooses cooperation. This situation usually occurs when the e-commerce financial institution is equipped with conditions for cooperation in the fastgrowing period. By acquisition and training of talents and arising attention and propaganda of the mainstream media, the e-commerce financial institution can attain the cognition of customers, who reap better experience than commercial banks, leading to a good reputation in the financial industry. Thus, the brand image and its propagation form a virtuous circle to strengthen the competitive power of e-commerce financial institution. However, due to being unsatisfied with distribution of cooperation interests, commercial banks are unwilling to choose cooperation and (competition, cooperation) can be taken as an evolutionary stable strategy in this period. (3) Consider A + A 1 +C 1 <0and B + βb C 2 <0 DetJ >0and Tr J < 0 (1, 0) is the ESS. Namely, A 1 <(A C 1 ) and βb C 2 < B (1, 0) is the ESS. Obviously, based on Table 2,theevolutionarystable strategy is that the commercial bank chooses cooperation and the e-commerce financial institution chooses competition. When the e-commerce financial institutions are unsatisfied with distribution of cooperation interests and have basic conditions of self-operation, they are not willing to choose cooperation with commercial banks but choose self-operation instead. It is definitely possible that commercial banks lose theirtalents,customers,capital,profits,andevenmarkets,if commercial banks operate and manage only in accordance with traditional thoughts of financial intermediaries, but not absorbing internet essence which is open, collaboration and sharing, and not paying enough attention to the customer experience and online service, especially to the analysis and use of customer information they owned. Because of all above, commercial banks choose cooperation to consolidate their main position in financial market, in order to maintain their sustainable development. Thus, (cooperation, competition) can be taken as an evolutionary stable strategy in this period. (4) Consider A αa+c 1 <0and B βb+c 2 <0 DetJ >0and Tr J < 0 (1, 1) is the ESS.

6 6 Discrete Dynamics in Nature and Society if CCB fails to cooperate, Alibaba achieved less net income when it chose noncooperation compared to cooperation. In conclusion, the game features in this period were in accordance with theoretical conclusion (2) and met the conditions of αa C 1 <Aand B 1 <B C 2.Thus,(noncooperation, cooperation) behaved as the ESS in this period. In fact, shortly after Alibaba required 2% of loan amount as its service fee, CCB refused the request for it would increase the burden of customers and add risks to the bank. Since then, collaborations between the bank and Alibaba gradually collapsed and finally ended. (3)Self-OperationStage:June2010 June2014.OnJune8,2010, Zhejiang Alibaba Microcredit Co., Ltd. was founded, marking the birth of the first big data-based e-commerce financial institution in China. On June 21, 2011, Chongqing Alibaba Microcredit Co., Ltd. was established. And on August 5, 2013, Chongqing Alibaba Small and Micro-Sized Small-Sum Loan Co., Ltd. went into run. The three microcredit corporations, whose registered capital totaled 1.8 billion yuan, were operated by Alibaba to conduct network credit loan business. As the first e-commerce customer-oriented microcredit corporation,alibabamicrocreditco.,ltd.(amcl)providedanew approach for small and microsized enterprises (SMEs) which were hard to obtain loans from commercial banks [26]. According to statistics of AMCL, the annual interest rate of loans was 18% 21%. The loan amount was not more than one million yuan and the term was not longer than one year. AMCL s CEO Sun Quan stated that the cost for each loan was 2.3 yuan while that of commercial banks reached 2,000 yuan approximately. By the first half of 2014, loans from AMCL had outnumbered210billionyuanintotaltofundover800,000 SMEs, the loan balance leveled 15 billion yuan, and the average balance for each SME was less than 40,000 yuan. The nonperforming ratio was assessed at 1%, lower than that for Chinese SMEs which was 2%. The funds of AMCL contained its own capital and those from nonbank financial institutions. The reason that why AMCLdidnotchoosebanksliedintwoaspects.Onone hand, the interest rate would move up 20% 30% on the basis of benchmark interest rate, pushing up financing cost. On the otherhand,theamountfrombankscouldnotmeettheneeds of AMCL. According to the Guiding Opinions of China Banking Regulatory Commission and the People s Bank of China on the Pilot Operation of Small-Sum Loan Companies released by China Banking Regulatory Commission, the balance of loans borrowed from banks by small-sum loan companies should not surpass 50% of its registered capital, asking that AMCL couldborrowatmost900millionyuanfrombanks.inother words, AMCL loaned 2.7 billion yuan from banks at most, causingittofailtosatisfyitsnetworkcreditloanbusiness obviously. Therefore, AMCL chose nonbank financial institutions including securities, funds, trusts, and insurances as external sources in the period of self-operation. On the basis of real-life data, the game strategies of AMCL and commercial banks were analyzed as follows: a network credit loan was set as N (N [1000, ]) with the term of one year, the annual interest rate of 20%, and the costforamcldealingwiththeloanof2.3yuan.thecostfor commercial banks to deal with a single loan reached 2,000 yuan and the one-year loan benchmark interest rate of commercial banks was pegged at 6% (July 6, 2012 November 21, 2014, the People s Bank of China). Suppose that AMCL tended not to cooperate; if commercial banks preferred noncooperation as well, the net income of the banks would be A 1 = 6%N When the banks were willing to cooperate and offer funds to AMCL, their net income was A C 1 =6%(1 + W%)N 2000, W [20%,30%].ItwasobviousthatA 1 <A C 1. Considering the noncooperation of AMCL, commercial banks would obtain more net income through choosing cooperation than that of noncooperation. Suppose commercial banks would choose cooperation; when AMCL preferred cooperation as well, its net income stood at βb C 2 = [20% 6%(1 + W%)]N 2.3, W [20%,30%]. When AMCL tended to noncooperation, its net income was B=20%N 2.3.ApparentlyβB C 2 <B;ifcommercialbankswouldliketocooperate,AMCLachievedmore net income when it chose noncooperation compared to that of cooperation. In conclusion, the features in this period were in line with theoretical conclusion (3) and met the conditions of A 1 <A C 1 and βb C 2 <B. Thus, (cooperation, noncooperation) became the ESS in this period. Actually, AMCL acquired capital mainly from asset securitization, through which the financing cost accounted for 6.5% 7% of the capital it achieved. The cost was lower compared with money borrowed from banks and the capital capacity borrowed from nonbank financial institutions reached several billion yuan. Therefore, AMCL did not establish cooperative relationship with commercial banks in this period. (4) Cooperation Stage: July 2014 to Date. OnJuly22,2014, AMCL and seven commercial banks including the Bank of China announced that they would conduct in-depth cooperationtoprovidebigdata-basedadvancedentrepreneurloan for SMEs. It was the first collateral-free credit loan that commercial banks offered on the basis of credit evaluation system supported by Alibaba s big data platform. The annual interest rate of the loan was 8% 14% in which 1% 2.5% served as the incomeofamcl.theloanamountrangedfromonemillion yuan to ten million yuan with the term of not longer than oneyear.byaugust22,2014,58enterpriseshadpassedaudits and loans from banks totally 120 million yuan approximately. With the adoption of real-life data, the game strategies of AMCL and commercial banks were analyzed as follows: set the amount of a network credit loan as N (N [ , ]),thetermofthatasoneyear,theannual interest rate as 8% in which 1% served as AMCL s income, and the cost for dealing with the loan as S. Without commercial banks collaboration, the one-year loan benchmark interest rate carried out 6% (July 6, 2012 November 21, 2014, the People s Bank of China) for the loan. Therefore, suppose AMCL to be willing to cooperate; then net incomes of commercial banks by acting uncooperatively and cooperatively would be A=6%N Sand αa C 1 =(8% 1%)N S = 7%N S, respectively. It was clear that A<αA C 1.Thatis,considering the cooperation of AMCL, commercial banks would obtain

8 8 Discrete Dynamics in Nature and Society quality. What is more, they should seek positively to cooperate with e-commerce financial institutions for win-win situation. (2) E-commerce financial institutions should further improve their own big data-based e-commerce customer credit evaluation system. On this fundamental, they should seek expansively to cooperate with the commercial banks and other nonbank financial institutions. Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper. Acknowledgment This work was supported by the National Natural Science Foundation of China (NSFC) (Grant no ). References [1] P. Xie and C. Zou, Research on internet based finance mode, Financial Research, no. 12, pp , [2] L. Mingxiong, T. Ying, and L. Yong, Internet Based Finance, China Financial & Economic Publishing House, Beijing, China, [3] H. Hailong, Research of the internet finance with the core as e- commerce platform, Shanghai Finance, no. 8, pp , [4] F. Lin, M. J. Shaw, and M. Y. Chuang, A unified framework for managing Web-based services, Information Systems and e- Business Management,vol.3,no.3,pp ,2005. [5] The 2013 Annual Chinese E-Commerce Market Data Monitoring Report,2014,http://www.100ec.cn/zt/2010bgdz/. [6] N. Yan and B. Sun, Mode innovation and of network financing for SMEs, Science Technology Progress and Policy, no. 3, pp. 1 5, [7] CheDeyun, The change of commercial banks coopetition strategy in the Internet financial evolution, International Finance, no.2,pp.7 10,2014. [8] X. W. Sun and J. L. Bao, Research on the innovation and development of the third-party B2B e-commerce model of China, in Proceedings of the 3rd International Conference on Advanced Computer Theory and Engineering (ICACTE 10), pp. V4-317 V4-319, Chengdu, China, August [9] R. Hinson, R. Boateng, and O. Jull Sorensen, E business financing: preliminary insights from a developing economy context, Information, Communication and Ethics in Society,vol.6,no.3,pp ,2008. [10] H. Zhaoyang, The research of collaborative competition, Journal of Central University of Finance & Economics, no. 2, pp , [11] M. Bengtsson and S. Kock, Coopetition in business networks: to cooperate and compete simultaneously, Industrial Marketing Management,vol.29,no.5,pp ,2000. [12] A. M. Brandenburger and B. J. Nalebuff, Coopetition, Bantam Doubleday, New York, NY, USA, [13] T. Lanjing, Reflections on the concerted strategy of cooperative enterprises, Theory Monthly, no. 11,pp , [14] A. M. Brandenburger and B. J. Nalebuff, The right game: use game theory to shape strategy, Harvard Business Review,no.7, pp.57 71,1995. [15]S.MiyuanandP.Yi, Stabilityanalysisonstrategyalliance, Industrial Engineering and Engineering Management, no.3,pp.76 78,2000. [16] O. Gomes, Discrete dynamics in evolutionary games, Discrete Dynamics in Nature and Society,vol.2012,ArticleID416789,23 pages, [17] J. W. Weibull, Evolutionary Game Theory, MIT Press, Cambridge, Mass, USA, [18] T. L. Friesz, R. Mookherjee, and M. A. Rigdon, An evolutionary game-theoretic model of network revenue management in oligopolistic competition, JournalofRevenue&PricingManagement,vol.4,no.2,pp ,2005. [19] M. D. Perez-Guirao, R. Luebben, T. Kaiser, and K. Jobmann, Evolutionary game theoretical approach for IR-UWB sensor networks, in Proceedings of the IEEE International Conference on Communications Workshops (ICC 08), pp , IEEE, Beijing, China, May [20] R.Yang,P.Shi,G.-P.Liu,andH.Gao, Network-basedfeedback control for systems with mixed delays based on quantization and dropout compensation, Automatica, vol. 47, no. 12, pp , [21] Y. Yang, J. Ma, and H. Tu, Chaotic characteristics and application of cooperative game and evolutionary game, Discrete Dynamics in Nature and Society, vol.2014,articleid908093, 13 pages, [22] OuBai, Governance of innovation network in the case of Alibaba, in Proceedings of the IEEE International Symposium on Management of Technology (ISMOT 12),pp.81 86,Zhejiang, China, November [23] P. Tao, Credit of small and micro businesses in the age of big data: concurrently the cooperation between bank and e-commerce companies, Times Finance, no. 5, pp , [24] D. Friedman, Evolutionary games in economics, Econometrica,vol.59,no.3,pp ,1991. [25] J. Yang, Z. Xu, J. Zhao, and Z. Ye, Comparison and enlightenment among three micro-credit models, Shanghai Finance, no. 9,pp.81 89,2010. [26] F.-R. Lin, R.-W. Po, and C. V. C. Orellan, Mining purchasing decision rules from service encounter data of retail chain stores, Information Systems and e-business Management, vol.9,no.2, pp ,2011.

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