Analysis on Cooperation and Competition Behavior of Enterprises Based on Evolutionary Game The Case Studies of Chinese Creative Industrial Clusters

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1 Advanced Materials Research Online: ISSN: , Vols , pp doi:0.4028/ 203 Trans Tech Publications, Switzerland Analysis on Cooperation and Competition Behavior of Enterprises Based on Evolutionary Game The Case Studies of Chinese Creative Industrial Clusters LI Jianshe, a, YAN Lewei 2,b,2 School of Management, Tianjin University of Technology, Tianjin , China a @63.com, b yanlewei202@63.com Keywords: Cooperation and competition behavior; Evolutionary Stable Strategy; evolutionary game; replicator dynamics equation Abstract. In recent years, not only the academics pays close attention to the creative industries, but also enterprises and the government keep a watchful eye on it. Cooperation and competition behaviors of enterprises will decide their competitiveness directly, thereby affecting the competitiveness and the future direction of our creative industries. In this paper, based on cooperation and competition behavior in creative industrial clusters, we establish a symmetric game model between two core enterprises and a asymmetric game model between the core enterprise and the adjacent down-stream one by using evolutionary game theory, then analyze its dynamic evolutionary procedure. The result shows that the system s evolutionary direction is closely related to players payoff, and influenced by cooperation profit, initial cost of the cooperation, capacity for independent innovation, cooperation successful rate and system s initial status. At last, some suggestions are offered for our government which can provide a theoretical basis for integrating creative industrial clusters. Introduction Michael E. Porter (2000) said Clusters are geographic concentrations of interconnected companies and institutions in a particular field. Clusters encompass an array of linked industries and other entities important to competition. They include, for example, suppliers of specialized inputs such as components, machinery, and services, and providers of specialized infrastructure []. Porter (998) also believes that a vibrant cluster can help companies in any industries use the most advanced technology and the most complicated manner to participate in competition [2]. The experiences of the development of creative industries in developed countries have proved that the development of cultural industry clusters can stands for the comprehensive competitiveness of cultural industry. Establishing cultural industry clusters is the key point for a country which wants to be a powerful one with cultural industries [3]. Domestic research on creative industry cluster mainly concentrated in the present situation of creative industries development, patterns and countermeasures [4,6];developments needed and dynamic of creative industries [7,8], formation mechanism research[9-].a large number of literatures show that our creative industry is still in its infancy, this study is to establish a symmetric game model between two core enterprises and a asymmetric game model between the core enterprise and the adjacent down-stream one by using evolutionary game theory, then it will analyze its dynamic evolutionary procedure. At last this paper may find out the key point of enterprise behavior to the evolution of clusters. Accordingly, we can reveal its development trend. Theoretical background and basic assumptions Evolutionary game theory is based on bounded rationality in economics, follows the basic principle of "natural selection", and studies the long-term structure change of "population". In evolutionary game, participants are limited rational, their choices are in the light of predecessors experiences, and their behaviors are affected by genetic factors, etc [2]. The core is the concept of "evolutionary stable strategy (ESS)" and "replication dynamics". Replication dynamics is to descript the dynamic All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-/05/6,03:37:08)

2 Advanced Materials Research Vols differential equation which expresses the frequency be used under some sort of strategy in a group. The strategy would be used widely when it has higher fitness, namely, "survival of the fittest" represents that the growth rate of the strategy is greater than zero [3]. "Evolutionary stable strategy (ESS)" must have two characters at the same time: a stable state that replication dynamic converged to; and the nature of the robustness of a small amount of error deviation [4]. This paper assumes that creative industry clusters in unstructured system, they evolved spontaneously by the principle of "survival of the fittest". Enterprises select and adjust their strategies according to the other members selections and their own relative adaptabilities. At the same time, they will make rapid responses to instabilities and uncertainties of the external environment, adjust the evolution path of the system through the transmission mechanism, and then, make the system more innovative. According to the nature of creative industries and the general rule of the evolution of industrial clusters, we assume that our creative industry is at the beginning of its whole life. At this stage, there are only some small-scale, connatural companies in clusters, when these clusters grow up; they will be made up of a few of core enterprises, a lot of small and medium-sized enterprises, and many intermediary organizations. When the clusters development to mature stage, they will have perfect ability to integrate internal resources, they will have their own "location brand", and let itself be social network agglomeration. Enterprises competition and cooperation in industry clusters includes two dimensions: horizontal symmetry game between enterprises in the same link of the value chain, asymmetric game between enterprises in different links of the value chain. As for simplification, we here defined the subjects of horizontal symmetry as two core enterprises (A and B) in upstream of the same link of the value chain; then defined the subjects of asymmetric game as one core company (A) in upstream and one non-core company in downstream(c). Horizontal symmetry evolutionary game Establishment of model At the beginning of the cultural creative industry cluster formation, Horizontal symmetry evolutionary game usually happens between core companies that have similar capacities. With the constant improvement of value chain, subjects will become ones in same links of the value chain. The objects of the model are core companies. On the one hand, their cooperation manifest as technology innovation cooperation, knowledge sharing and so on, on the other hand, their competition manifest as independent technological innovation, no knowledge sharing. The behavior of game is similar to croak game [5]. The basic meaning of it is the same type of male frogs in same conditions can attracted females if they sing alone, however, they may make themselves in danger and cost energies. If they sing together, more females can be attracted, and reduce a lot of energies. The excess profit matrix in creative enterprises cooperation and competition based on croak game is shown in Table. Table The excess profit matrix in both sides A cooperation competition B cooperation ip- C, ip- C M- C, - M competition -M, M- C 0, 0 Variable description: in the payoff matrix, P is excess return when both A and B choose "cooperation" (M<P<), i is probability for successful cooperation between A and B; C is upfront costs for cooperation( including transaction costs, etc), namely, initial costs; M is return when one of them chooses "cooperation" (0<M<), -M is return for the other s free ride. Hypothesis: the proportion of businesses choose cooperation strategy for "x", proportion of businesses choose competition strategy for "-x", then, their expectative extra profits and the average extra profit can be expressed: U =x(ip-c)+(-x)(m-c)

3 950 Advances in Applied Science and Industrial Technology U 2 =x(-m) U=xU +(-x)u 2 Replicated dynamic equation based on the above benefit is: dx/dt=x(u - U)=x(-x)[x(iP-C-+M)+(-X)(M-C)], When dx/dt=0,we can get three local equilibrium:x =0,x 2 =,x 3 =M-C/-iP [0,] dx dt x dx dt M C 0 ip x Chart Dynamic phase image(m-c/-ip<0) Chart 2 Dynamic phase image(0<m-c/-ip<) dx dt 0 x Chart 3 Dynamic phase image (M-C/-iP>) ()when M-C/-iP < 0(M < C),x 3 < 0,the efficient equilibrium are x and x 2,then, the corresponding replicated dynamic equation of phase image is shown in chart. From chart, we can find that x =0 is the only ESS, that means when one of the two chooses "cooperation", and its extra profits (M) is less than the initial costs(c), all enterprises in the cluster will choose "competition". In other words, competition is the eventual result in a long-term dynamic tend as long as there is a company chooses competition strategy. Even though all choose cooperation strategies, only few of them change the strategy, others are tend to change too, "competition" strategy will be the final choice. (2)when 0 < M-C/-iP < (M > C, and ip-c < -M),The above three replicated dynamic equilibriums are reasonable, because they all in the effective range of 0 x, the corresponding replicated dynamic equation of phase image as chart 2. From chart 2, we can find that x 3 =0 is the only ESS that means when one of the two chooses "cooperation", and its extra profits (M) is more than the initial costs(c), and when both all choose "cooperation", the extra return (ip-c) is less than extra profit of free ride (-M), companies in the cluster may choose "cooperation", and also have possibilities to choose "competition". (3)when M-C/-iP>(iP-C>-M),The above replicated dynamic reasonable equilibriums are x and x 2,the corresponding replicated dynamic equation of phase image as chart 3. From chart 3, we can find that,x 2 =0 is the ESS, namely, when the extra return (ip-c) is more than extra profit of free ride(-m), Cooperation is the eventual result in a long-term dynamic tend as long as there is one company chooses cooperation strategy

4 Advanced Materials Research Vols Model analysis Form the game model, we can get the conclusion: the result of long-term evolution is not regular. It is classified into perfect competition, perfect cooperation, and competitive cooperation. Which path it on earth will choose is closely related to the extra benefit matrix. Moreover, under the certain information guiding mechanism, which equilibrium will be converged is affected by the initial state of the game. The stability of the perfect competition strategy described by chart appears at the beginning stage of creative industries, the effect on low-cost cannot happen, and the concentration is not appear too; The stability of the perfect cooperation strategy described by chart 3 appears in mature period, At this stage, clusters have perfect information communication platform and well protection of intellectual property rights, etc. Above the two conditions are extreme ones. Under the present economic situation, the behavior of companies in the cluster should be competitive cooperation that be descried by chart 2. At stable state, the proportion of choosing cooperation strategies in proportion to additional income got from independent innovation (M), cooperation benefits (P) and the proportion of successful cooperation (i), and in inverse proportion to the initial costs created by cooperation (C). () The proportion of successful cooperation (i) is decided by innovation capabilities and the sincerity for cooperation. The stronger the innovation capabilities and the team spirit, the bigger the i will be. (2) The initial costs created by cooperation (C) include costs for choosing each other and assessing partnerships. It depends on the degree of the network information platform in the cluster. (3) In the case of certain cooperation cost and innovation capabilities, additional profits created by cooperation are disturbed by the market, the government policies, and the industry-wide earning ratio. (4) Independent innovation (M) is not only decided by their own knowledge level and innovation abilities, but also depends on the degree of the protection of intellectual property rights. The more perfect the protection is, the bigger the M is. The less the "free ride" is, the easier the cooperation to come true. Longitudinal asymmetric evolutionary game Establishment of model When creative industries come into the growth period and the mature period, the internal value chain will be improved. The number of medium-sized enterprises in the middle and down stream will increase, and their relations will become closely. They want to share information and technology with each other, to cultivate their own core competence, and to cooperate with others in the non-core capabilities. Therefore, competitive cooperation will appear between enterprises of adjacent link in this stage. The excess profit matrix in creative enterprises cooperation and competition based on croak game is shown in Table 2 C A Table 2 The excess profit matrix in both sides Cooperation Competition Cooperation M C +P C - D C, P A +M A -D A M C - D C, M A Competition M C, M A - D A M C, M A

5 952 Advances in Applied Science and Industrial Technology Variable description: in the payoff matrix, M C and M A are expressed as normal return when A and C all choose "competition", P C and P A is extra profits when A and C all choose "cooperation", we assume that P C,P A >0, D C and D A are initial costs when A and C all choose "cooperation". Hypothesis: the proportion of subject "A" choosing cooperation strategy for "x", the proportion of choosing competition strategy for "-x", the proportion of non-core subject choosing cooperation strategy for "y", the proportion of choosing competition strategy for "-y". Then, extra cooperative profits of A can be expressed: U =y(m A +P A -D A )+(-y)(m A -D A ) () Extra competitive profits of A can be expressed: U =ym A +(-y)m A (2) Average extra profit of A is:u=xu +(-x)u 2 (3) Therefore, based on equation(),(3)and the replication dynamic differential equation, we can get the repeated dynamic equation of A : dx/dt=x(u -U)=x(-x)(P A y-d A ) (4) Similarly, the repeated dynamic equation of C: dy/dt=y(-y)(p c x-d c ) (5) Differential equations(4) and (5)described the trend of this adaptive system, when dx/dt=0, dy/dt=0,we can get five local equilibrium:o(0,0),a(,0),b(,0),c(,),d(x*,y*) and, x*=d C /P C, y*=d A /P A and (x*,y*) (0,) (6) According to the method proposed by Friedman (99), the stability of the equilibrium can be got ( - 2x)( PAy DA ) x( x) PA J = ( ) by analyzing its Jacobian Matrix [8] : y( y) P C ( 2y) PCx DC Model analysis Form the game model, we can get the conclusion: the result of long-term evolution is not regular. It is classified into perfect competition, perfect cooperation, and competitive cooperation. Which path it on earth will choose is closely related to the extra benefit matrix. Moreover, under the certain information guiding mechanism, which equilibrium the system will be converged is affected by the initial state. Therefore, in the process of the game, some parameters of the initial value and their changes make the equilibrium different. r: payoff-risk coefficient of the core company A, r2: payoff-risk coefficient of the core company C, a: effective resource value A contribute to, a2: effective resource value C contribute to. r, r2 > 0,a,a2 >0,then, PA= r a2,pc = r2 a (7) DC DA By(6)and(7): x* =, y* = (8) ra ra 2 2 From(8),we learn that parameters that affect the system evolution are: initial costs, yield coefficient, and effective resource value both contribute to. We should discuss respectively. ()Payoff-risk coefficient r, r2.from chart 4, we learn that the bigger the earnings coefficient is, the bigger the area of ACBD is. Then, the probability that converges to equilibrium C is bigger too. In practice, it requires the enterprises to cultivate their own core ability, to delegated non-core parts to other capable partners, so that strengthen the relations inside the company, and with other partners. (2)Initial costs DC,DA.. The smaller initial cost is, the bigger the area ACBD is. Then companies tend to choose cooperation strategy, and the system tends to converge to the equilibrium C. (3) Effective resource value a, a2. Core companies in creative industries clusters, core companies always in the upstream of the value chain. Its contribution to the resource value is far greater than that of non-core enterprise resource, so a>a2

6 Advanced Materials Research Vols Summary In the early part of the creative industry clusters, the government needs to establish good enterprise behavior system and reasonable financing mechanism. When the clusters come to growth period, enterprises and the government should attach more importance to the absorption and cultivation of talents, strengthening the enforcement of norms as well. When the clusters enter the mature stage, the work of the government should tend to be restrictions on small enterprises to enter. While encouraging the integration between creative industries and other industries, the government are maintaining the cluster value, optimizing the industrial value chain, and improving the competitiveness of the creative industry. Literature References [] Ivan Turok. Cities.European Planning Studies, Vol. (2003), No.5, p [2] Michael E Porter. Harvard Business Review, (998), p 9-0 [3] Zheng ZiLi.. Journal of Nanjing University of Finance and Economics,Vol.3(202), p (In [4] DONG Ke-chao WANG Juan. Shanxi Architecture, Vol.38 (202), No.28, p. -4 [5] ZHAO Hong,WANG Jun-hong. Journal of Beijing Institute of Economic Management,Vol.2 (2006), No.28 p.3-6. (In [6] ZHAO Ying-fang. Oriental Forum, Vol.3 (2009), p (In [7] HUA Jian. Journal of Shanghai University of Finance and Economics, Vol.9 ( 2007), No.4, p.3-3. (In [8] ZHANG Wei XIE Yu-hong. Industrial Economic Review,Vol.5 ( 202), p (In [9] HU Bin. China Industrial Economy, Vol.5 (2007), p (In [0] Wu Yan, Chen Qiuling. Economic Tribune, Vol.0 (2006), p (In [] Chen Jianjun,Ge Baoqin. Contemporary Economy & Management,Vol.9 ( 2008), p (In [2] Yu Weisheng. Game Theory and Economics Higher Education Press Publishing, Beijing, China, (2007), in press. (In [3] Mao Lei. Science & Technology Progress and Policy, Vol.27 (200), No.8, p (In [4] Tian Zhonghe,Sun Quan. Science & Technology Progress and Policy,Vol.3 ( 202), p (In [5] Xie Zhiyu. Economic game theory Fudan University publishing house, Shanghai, China, (200)

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