Evolution of knowledge sharing behavior in social commerce: An agent-based computational approach

Information Sciences xxx (2014) xxx–xxx

Contents lists available at ScienceDirect

Information Sciences journal homepage: www.elsevier.com/locate/ins

Evolution of knowledge sharing behavior in social commerce: An agent-based computational approach Guoyin Jiang a,b,⇑, Feicheng Ma b, Jennifer Shang c, Patrick Y.K. Chau d a

School of Information Management, Hubei University of Economics, Wuhan 430205, China School of Information Management, Wuhan University, Wuhan 430073, China c Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260, United States d School of business administration, The University of Hong Kong, Hong Kong, China b

a r t i c l e

i n f o

Article history: Received 8 July 2013 Received in revised form 30 October 2013 Accepted 13 March 2014 Available online xxxx Keywords: Social commerce Knowledge sharing Dynamic evolution Computational experiment

a b s t r a c t The rapid development of e-commerce has expedited knowledge growth in the e-commerce social community. Knowledge sharing among online users has exhibited a nonlinear dynamic evolution. This paper examines the evolutionary process of knowledge sharing among users of the social commerce; builds an evolutionary game model to depict knowledge sharing phenomenon in the virtual community; and develops a mixed learning algorithm based on individual user’s historical game strategy, neighborhood user’s strategy, and information noise. We design a computational model based on multi-agent theory and social network, and implement computational experimental system using NetLogo 5.0. We find that the proposed computational–experimental model can help decision makers simulate evolutionary process under various scenarios. The evolutionary game rule and social network structure significantly influence the degree of cooperation and knowledge sharing among users. The greater noise the network information has the less stable the users’ behavior will be. One can thus identify an optimal initial cooperation rate to facilitate the system to reach equilibrium state quickly. Our study on the dynamic evolution of knowledge sharing behavior in the social commerce contributes to the theoretical development of literature and provides valuable decision-making support to managers. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction The emergence of Web 2.0 has changed the way users and enterprises interact and collaborate with each other. It creates social commerce by combining social media, social network and e-commerce. Social commerce is filled with social interactions and users in the online commerce community and other social network rate and share online product information and advice [1]. Individual opinions earnestly contributed to the online community have enhanced knowledge sharing and steered new consumer behavior. iResearch (www.iresearch.com) reports that the online shopping behavior of social media users have significantly changed in recent time, as (i) the community of seeking friends online is growing rapidly; (ii) social media users pay more attention to ‘‘acquaintance’’, and are more confident of friends’ comments as they are often skeptical of advertising claims; and (iii) the integrated e-commerce and social media can re-sort the user’s social relationships, and effectively motivate the ⇑ Corresponding author at: School of Information Management, Hubei University of Economics, Wuhan 430205, China. Tel.: +86 27 81972191. E-mail address: [email protected] (G. Jiang). http://dx.doi.org/10.1016/j.ins.2014.03.051 0020-0255/Ó 2014 Elsevier Inc. All rights reserved.

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product spread and form virtuous circle [2]. In particular, iResearch revealed that 54% of social media users respond that they would purchase a product if their friends ‘‘like’’ it, as opposed to 28% of the overall e-shoppers. Social commerce exemplifies a collaborative environment where people share information and resources, so that the total effect is greater than the sum of individual effects. The users in social commerce can influence the buying behavior of others by word of mouth, recommendation and transfer of knowledge on the social network [3]. Examples of social commerce can be found in. Pinterest (www.pinterest.com), ebay community (community.ebay.com), and taobao froum (bbs.taobao.com). Users can quickly access and readily capture other peoples’ experiences and derive comprehensive and relevant information about the merchandise. In short, knowledge exchange has inundated the social commerce and effective knowledge management is crucial for enhancing e-commerce performance. However, there is a dearth of research directed toward optimizing knowledge sharing in social commerce [4]. Few studies have empirically examined what drives continued knowledge sharing [5,6], but none have explored the evolution issues from the perspective of mathematical modeling and simulation approach in social commerce. Registered users in social commerce build their networks by publishing shopping and answering shopping posts. Users can easily see the remarks, reply, and comments of other users. For example, a registered user in the discussion forum can quickly locate the posts of connected users after log-on. Users may share real knowledge, reserve or even distort facts, and even post incomplete or inaccurate information. A user often becomes more active over time; their remarks and replies increase network knowledge and before long the network would form a nonlinear evolutionary state. Users can choose knowledge sharing strategies (actual experience or unreal shopping information) based on their own preference and others’ actions. They may choose a strategy now, adopt a different one later, and use a combination strategy at the end. The e-commerce administrator thus should decide on what management strategies suit the network structure and user behaviors best. The knowledge sharing behavior among users in a social commerce exemplifies the evolution of knowledge interactions over time. In this research, we employ agent-based computational approach to explore the dynamic evolutionary process of knowledge sharing among users of the social commerce. The goals of this study is to (1) model user interactions in the social commerce using game theory and identify the equilibrium of the dynamic evolution; (2) build a computational model to study the behavioral evolution of knowledge sharing in social commerce based on evolutionary game, multi-agent, and social network theory; and (3) analyze how management strategies affect e-commerce discussion forums, and how to select knowledge sharing network structures; examine how network parameters and information transparency shape the evolutionary equilibrium. In short, we seek to provide mechanisms for social commerce administrators to establish knowledge sharing strategy and manage under different scenario. Our paper is organized as follows. In Section 2, we review the extant literature. Section 3 proposes a theoretical model and develops a dynamic methodology to help reach evolutionary equilibrium. In Section 4, we conduct computational study to validate the proposed model and understand the evolution of knowledge sharing in e-commerce. Section 5 presents computational results through virtual experiment, while the implications, limitations, and suggestions for future work are given in Section 6. Section 7 concludes this research.

2. Literature reviews 2.1. Virtual community and social commerce In social commerce, people communicate with each other through electronic media [7]. The virtual community comprises people, intention of sharing, policy, and computer system [8]. Bhattacherjee [9] defines a virtual community as one gathering rational community users, interacting with virtual spaces, and sharing among users. Therefore, obtaining knowledge through information collection and user interactions is a key feature of a virtual community. The e-commerce forum offers a special virtual community, which can integrate social features and enhance e-commerce performance.

2.2. Knowledge sharing in virtual community Literature on knowledge sharing in a virtual community abounds. Most researchers have examined the drivers affecting the participation in the community, and found individual motives include internal, external, and social motives [10–12]. These factors affect the initial motivation of users joining the community for knowledge sharing [11,12]. Yet, the initial motives may not continue. Few studies focus on the influence of trust instead of motives on users’ continuous participation of the virtual community [5]. In fact, social learning takes place during the virtual community involvement, and users may alter their motivation. Sun et al. [6] find that task complexity and self-efficacy (two social learning factors) moderate the relationship between motivation and sustained participation. The transactional complexity and the exterior motive have a negative correlation, whereas complexity and the interior motive have a positive non-linear relationship. Existing studies assume users’ continuing participation in virtual community is monocyclic and static [5,6]. However, the continuous knowledge accumulation, expansion and interaction is a dynamic evolutionary process. Its evolutionary strategy has a significant influence on organizational performance. An optimal strategy to knowledge evolution significantly aid the accumulation and improvement of knowledge [13]. Few literature on users’ continuous participation is based on the theory Please cite this article in press as: G. Jiang et al., Evolution of knowledge sharing behavior in social commerce: An agent-based computational approach, Inform. Sci. (2014), http://dx.doi.org/10.1016/j.ins.2014.03.051

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of social relationship [14]. As knowledge sharing creates value, investigating knowledge sharing in a virtual community from the economic perspective is a fitting attempt to explain the drive of knowledge sharing in social commerce. 2.3. Modeling knowledge sharing through game theory Samieh and Wahba [15] studies knowledge sharing in the virtual community through game theory and shows that the payoff for knowledge sharing among individuals can be described by multi-party game. Shih et al. [16] claims that learning type and stimulus affect knowledge sharing in a cooperative team. Bandyopadhyay and Pathak [17] build an interactive game model between the contractee and the contractor, and conclude that sharing complementary knowledge could boost performance. Cai and Kock [18] use game to model e-collaborative evolution and identify strategies that would improve joint performance. Ding and Huang [19] concludes, through a game framework, that collaboration is beneficial to knowledge creation, while certain injection ratio of leaders and followers may render unstable collaboration. Li and Jhang-Li [20] find that knowledge benefits can be improved by IT investment and stimulus mechanism, while decision-maker’s preferences and information integrity affect knowledge sharing. Information shared in social commerce may be true, overstated, or misleading. If users can build a trusting and cooperative relationship, the information published or recommended may be trustworthy. If they deviate from the tenet of knowledge sharing, the information may be deceptive and hurt social commerce users. Prior research has shown that network topology and social factors significantly impact consumers’ decision-making process [21]. Choi et al. [22] investigated how network structure impacts the dynamics of innovation diffusion, while others show that different network structures (e.g. small-world, random, and scale-free) have distinct influences on cooperative behavior [23–25]. Nowak and May [26] study evolutionary game structure based on prisoner’s dilemma and conclude that a regular lattice facilitates the cooperative behavior [26]. Hauert and Doebeli [27] show that the spatial topological structure in the snow drift game inhibits the emergence of cooperative behaviors. In these studies, the users are defined as nodes and every node in the network has only one state. It holds one state toward its neighboring node either via cooperation or defection. However, in social commerce, each agent (user) interacts with multiple users and implements different strategies toward them under different circumstances. So an agent may choose a cooperation strategy toward neighbor A, and pick a defection strategy against neighbor B [26,28,29]. 2.4. Investigating the evolutionary process based on computational method Computational experiments, such as multi-agent model, help one to understand the complexity, dynamics and adaptiveness of a knowledge sharing system [30]. They are well-suited to study evolutionary behavior [31,32], as they describe the autonomy, interaction, reactivity and reasoning behavior of complex systems. Traditional game theories generate macro-level (general) conclusions, while the evolutionary game and agent-based computational experiments we adapted in this study would bring micro level (specific) results to the social commerce study. The traditional evolutionary game method models macro-level evolution of games between two populations: one holds a cooperation strategy and the other adopts a defection strategy. However, the evolutionary game model cannot represent individual interactions. A well-suited approach for modeling micro-level individual interactions is the agent-based simulation. Through detailed modeling, the agent-based simulation can ultimately provide informative macro-level summary and offer valuable managerial implications. In this research, we employ a unified computational experiment framework by integrating multiple agents, evolutionary game, and social network to study the cooperation and defection strategies among users under different game rules and network structures. By examining the path strategy (the combined past strategies) and evolutionary equilibrium, we contribute to the behavioral evolution theory of knowledge sharing in the virtual community and offer decision support for management practice in social commerce. 3. Theoretical model for knowledge sharing in social commerce 3.1. The game theory based model Knowledge sharing strategies among users are affected by the experience they accumulated, their perception of other users’ knowledge sharing behaviors, and changes in the external setting. The behavior of knowledge sharing in the social

Table 1 Game payoff matrix with penalty parameters. Player 1

Cooperation Defection

Player 2 Cooperation

Defection

b  c/2, bc/2 b  d, b  c,

b  c, b  d 0, 0

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commerce can be expressed by the interactive game relationship. Table 1 gives a symmetric game payoff matrix, which includes a social punishment. In Table 1, the b stands for the benefit of knowledge sharing, c is the expense of knowledge sharing, while d is the loss of giving trust to flawed information in knowledge sharing. For instance, in ebay community a recognized fault can be published, as evidenced in the community content policy: http://pages.ebay.com/help/policies/user-created-content-ov.html. The transformation of knowledge sharing behavior in social commerce indeed is a game process evolved in the user group over time based on the game payoff matrix. 3.2. Identifying evolutionary equilibrium through dynamic replication The evolutionary game equilibrium can be detected by the dynamic replication method [33,34]. This method can provide theoretical support for management to make macroscopic decisions on knowledge dispersion, regardless of network structure and environmental factors. Let P be the percentage of community users holding a cooperative attitude. Then, the expected cooperation benefit from knowledge sharing can be expressed as:

Ec ¼ Pðb  c=2Þ þ ð1  PÞðb  cÞ

ð1Þ

The expected benefit of defection from knowledge sharing is Ed:

Ed ¼ Pðb  dÞ

ð2Þ

The average benefit of this group is E:

E ¼ P  Ec þ ð1  PÞ  Ed

ð3Þ

From dynamic replication, we find the state of the evolutionary system over time can be expressed as:

h c  i dP ¼ PðEc  EÞ ¼ Pð1  PÞðEc  EdÞ ¼ Pð1  PÞ P þ d  b  ðc  bÞ dt 2

ð4Þ

Therefore, the evolutionary system has three possible solutions to game equilibrium.

cb ; þdb 2

P ¼ 0; 1; c

and



P ¼

 cb c þdb 2

ð5Þ

From Eqs. (3)–(5), we are able to determine the equilibrium of the game under different scenarios. We summarize them in Propositions 1-3 below. Proposition 1. If any of the following scenario conditions are met, the group evolutionary equilibrium will reach ‘‘defection’’.

(c ðScenario 1Þ

2

P P 1

(c ðScenario 2Þ

þdb>0

2

þdb<0

P60

(c ;

i:e:

2

(c ;

8c þdb>0 > > <2 ðScenario 3Þ 0 < P < 1 ; > > : P0 < P

i:e:

þdb>0

b < c; c P 2d 2

þdb<0

b 6 c; c > 2d

8c þdb>0 > > <2 i:e: b < c < 2d > > : P0 < P

Proof. See Appendix A.1. h Proposition 2. If any of the following scenario conditions are satisfied, the group evolutionary equilibrium will reach ‘‘cooperation’’.

(c ðScenario 4Þ

2



P P1

(c ðScenario 5Þ

þdb<0

2

þdb>0 

P 60

(c ;

i:e:

2

b > c; c 6 2d (c

;

i:e:

þdb<0

2

þdb>0

b P c; c < 2d

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8c > <2 þ d b > 0 ðScenario 6Þ 0 < P  < 1 ; > : P0 > P

8c > <2 þ d  b > 0 i:e: b < c < 2d > : P0 > P

Proof. See Appendix A.2. h Proposition 3. If the conditions in Scenario 7 are satisfied, we will find the equilibrium is at P = P⁄.

c þdb <0 ; ðScenario 7Þ 2 0 < P < 1

c

2

i:e:

þdb <0

b > c > 2d

Proof. See Appendix A.3. h Using the dynamic replication method (see Appendix A) to solve evolutionary game for knowledge sharing in social commerce can help design the knowledge sharing mechanisms in a macro-environment, regardless of the network structure and information noise. However, in a knowledge sharing game, the evolutionary result is not a simple accumulation of all game states held in a single time period. The historical game path, interactive users’ decisions and information noise, need to be taken into account comprehensively. Such evolution has non-linear features. Thus, the evolutionary equilibrium cannot be simply determined by the traditional dynamic replication method. It has to be analyzed by the computational–experimental method from the perspective of agency theory, game theory, and social network. 4. The computational model 4.1. Combination of game strategies among social commerce users When an agent in the social network interacts with a neighbor user during a time period of knowledge sharing, she may hold a cooperation or defection strategy. She may follow a different strategy in the next time period. The choice of strategy depends on her own as well as the decisions of other users. Fig. 1 shows the eight possible strategy paths. FS(t) is the strategy chosen by the user at term t. NS(t) is the strategy chosen by her neighbor user at time t. Depending on her own strategy and her neighbor’s strategy choice, she will pick one of the eight strategy paths for time t + 1. 4.2. The game learning algorithm for users in the social commerce The strategy chosen by an agent at time t depends on the strategy of the neighboring users at time (t  1) and the agent’s own strategy. Learning algorithms for the evolutionary game include random process and heterogeneous group mixed learning algorithm [35]. The learning algorithm chosen in this study resembles the learning method seen in the dynamic replication method. That is, a game player will imitate the behavior of the other game player, who attained the highest profit in the previous time period. Note that we do not examine the imitation of single strategy a user employed but to consider the path of strategies she adopted thus far.

FS(t) Defection

Cooperation NS(t)

NS(t) Defection

Cooperation

Cooperation

FS(t+1)

FS(t+1)

Defection Cooperation CCC

CDC

FS(t+1)

Defection

Cooperation CCD

FS(t+1)

Defection

Defection Defection Cooperation Cooperation

CDD

DCC

DCD

DDC

DDD

Fig. 1. The eight path strategies from time t to t + 1.

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In the knowledge sharing game, an individual learns from the neighbor with the highest benefit, following the stochastic process expressed in Eq. (6):

Pðj ! iÞ ¼

1 1 þ eðuj ui Þ=k

ð6Þ

where uj is the benefit generated by agent j and it is the maximum among those accrued by neighborhood users, while ui is the accumulated benefits of agent i and k is the information noise [36]. When k is very large (very noisy), say approaching 1, P will approximate ½, equivalent to the result of coin-tossing. On the other hand, when k is very small (e.g. approaching 0), the values of P will be close to 1, indicating agent i is sure to imitate user j. 4.3. Percentage of cooperation and defection In our study, a node in the network is either in a cooperation- or defection-state. We define the % of cooperation in a network as

% of cooperation ¼

sum of the nodes holding the cooperation strategy  100%; 2  total number of connections

and the % of defection in a network as

% of defection ¼

sum of the nodes holding the defection strategy  100% 2  total number of connections

4.4. Formalize the social commerce 4.4.1. Define the dimensions of a social commerce network Newman [37] maintains that a complex network such as a social network possesses the small-world features, where most users are not direct neighbors of one another, but they can be reached from a small number of hops or steps. By applying data mining techniques to the data collected from Taobao (the largest Chinese e-commerce firm) forum, we find that the social commerce does share the features of a small-world and the nature of a scale-free network, which has a degree distribution following a power law [37,38]. The two sets of data we collected from the Taobao forum include one with 554 nodes (Sample A), and the other with 1073 nodes (Sample B). Using Ucinet 6, we attain the following statistical characteristics: (1) Average path length. An average path length is the average number of steps between node i and node j, along the shortest paths dij. It is a measure of the efficiency of information or mass transport on a network [39].

X 1 dij NðN þ 1Þ 2 iPj

L¼1

ð7Þ

where N is the number of nodes in the network. A small L indicates that information can be communicated more directly and easily. Most real life networks have a very short path length leading to the concept of a small world where everyone is connected to everyone else through a very short path. For Samples A and B, the average path length is 3.026 and 2.356 respectively. We found the path lengths are comparable and both samples are relatively small, and only 2–3 links will connect the agent to the target user. (2) Network clustering coefficient. In social commerce, nodes often intertwine and generate groups with high degree of ties. A network clustering coefficient is a measure of degree to which nodes in a network tend to cluster together [39]. It is usually between 0 and 1, and a fully connected network has a clustering coefficient of 1. We found the weighted clustering coefficients of our two samples are 0.829 and 0.790 respectively. Both are large and comparable. (3) Degree distribution. The degree of a node in a network is the number of edges the node has connecting to other nodes. We define the degree distribution as the probability distribution of these edges over the whole network. We found the maximum degree of Sample A is 43, while that of Sample B is 95. The minimum degree in each sample is 1. Fig. 2 shows the degree distribution of the two samples, while Table 2 identifies the most appropriate model to fit the observe degree distribution. We found that the Power Model fits the degree distribution data best and no significant differences are found between the two samples. Our analysis above shows that the social commerce has the ‘‘feature of the small-world’’, which indicates it has a short average path length and a large Network clustering coefficient; and its degree distribution obeys the power law. Due to these three characteristics, we conclude that the network structure of the studied social commerce is a scale-free network. Please cite this article in press as: G. Jiang et al., Evolution of knowledge sharing behavior in social commerce: An agent-based computational approach, Inform. Sci. (2014), http://dx.doi.org/10.1016/j.ins.2014.03.051

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Fig. 2. Degree distribution of the two samples.

Table 2 Results of curving fitting. Equation

Model summary

Parameter estimates

R2

F

df1

df2

Sig.

Constant

b1

Power

.618

30.734

1

19

.000

36.069

1.156

Sample A Exponential Logistic

.292 .292

7.850 7.850

1 1

19 19

.011 .011

6.836 .146

.069 1.071

Power

.558

42.986

1

34

.000

37.021

.962

Sample B Exponential Logistic

.184 .184

7.670 7.670

1 1

34 34

.009 .009

4.450 .225

.024 1.024

In view of the limited sample data we collected, we feel it may be necessary to examine the evolution of knowledge sharing under the small-world network and random network in our research, in addition to the scale-free network structure associated with our two samples.

4.4.2. Formalize the model definition Let each node in the virtual network be an agent and there are n agents. We define the community network N as N = {X, ST, NT, NB, FI, F, t}, in which, (1) X is the set of agents and X = {agent1, agent2, . . . , agentn}. Each agent is a user in the network. (2) ST is the state space with ST = {ST1, ST2, . . . , STj, . . . , ST8}. Each STj, is a path strategy. (3) NT is the set of network types and NT = {Smallword, Random, Scalefree}. These three network structures exemplify the classic complex networks discussed in literature [37]. NT (4) NB is the state space of all neighbors of an agent. NB = {NB1, NB2, . . . , NBn}, where NBi ¼ fagenti ! agentj g. Namely, NB comprises users neighboring agent i in the NT network structure. (5) FI is the set of benefits derived by all agents, FI = {FI1, FI2, . . . , FIn}. (6) F is the state transfer function. F: {(FIi, NBi) ? ST(t)}  t ? ST(t+1). The state of agent i at time t + 1 is a function of parameters, including its own profit, game strategy, and the strategies of other users who have direct connection with agent i at time t.

5. Computational–experimental system and virtual experiment In this section, we design the computational system, simulate the virtual community and evolutionary process, collect numerical results under different scenarios, and make comparisons through statistical analysis. The simulation and experiments are implemented by NetLogo 5.0. Please cite this article in press as: G. Jiang et al., Evolution of knowledge sharing behavior in social commerce: An agent-based computational approach, Inform. Sci. (2014), http://dx.doi.org/10.1016/j.ins.2014.03.051

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5.1. Experimental system and the default parameters We build an agent-based model to explore the interactions among all individuals over time (200 time periods in our case). The experimental system is divided into four modules: (1) (2) (3) (4)

Set up the network, and define the game parameters and the model parameters. Graphically illustrate the network evolution, and show how the nodes change dynamically in the network. Display the results, and show the characteristics of the network (e.g. clustering coefficient and path length). Draw the strategy evolution curve.

The parameters given in Table 3 are an example setting of scenario #1. Those values are determined by the conditions shown under scenario #1 in Proposition 1. We can manually change the parameter settings when different simulation is experimented to address a new scenario. 5.2. Experimental results under different game parameters and network structures We study eight path strategies: CDC, DDD, CDD, DCD, CCD, CCC, DCC, DDC, as discussed in Fig. 1. Each agent in the network connects with one or more agents (users). Each agent has his own game strategy toward different agents. For example, he may have a cooperation relationship with the jth user in the neighborhood but have a defection strategy with neighbor k. Therefore, each agent may employ one or more path strategies. Recall in Section 3.2 we divide the social commerce into seven scenarios. We replicate each scenario 50 times (sample size of 50) so as to ensure the reliability of the experimental results. The length of each simulation cycle is set to 200 time periods. We explore the evolution of knowledge sharing using the simulated data and compare the results with the theoretical results in Propositions 1-3. We first employ ANOVA to test the differences in means and variances at a 95% confidence level. When p-value <0.05, we conclude there is significant difference between the tested populations. As we cannot guarantee that the simulated results are normally distributed, we also employ the Kruskal–Wallis H (a non-parametric) approach to test if samples are originated from the same population. When p-value >0.05, we conclude that there is no significant difference in population distributions. For Scenario 1, to satisfy the condition: b < c, c > 2d, we assume b = 6, c = 10, and d = 4. The results are summarized in Fig. 3. Fig 3(a), (c), and (e) shows the changes in the % of cooperation and defection over time, while Fig. 3(b), (d) and (f) display the number of nodes holding the cooperation strategy under each path strategy in each network structures. From Fig. 3(a), (c), and (e), we find defection is the dominant strategy in the game, which can quickly reach equilibrium at time period 10. The result of the simulation is consistent with the macro-trend found in Proposition 1. From Fig. 3(b), (d) and (f), we find path strategies CDC and CDD dominate others. The path strategy CDC is an amicable strategy combination, as the agent holds a cooperation strategy at first. Even though his opponent reacts with defection strategy, he still insists on applying the cooperation strategy subsequently. Path strategy CDD has a Tit for Tat relationship, where the agent will use cooperation strategy at first, then replicate opponent’s action and employ defection strategy. Path strategy CDD will affect users who opt to take the defection initiative. Under Scenario 1, the means of % cooperation on small-world, random, and scale-free networks respectively are 34, 34.37, and 41.79. The p-value from ANOVA mean test is 0.00, indicating the means among the three network structures are significantly different. Alternatively, the standard deviations are 6.17, 5.66, and 7.08 respectively. The homogeneity test results in a p-value of 0.00 (<0.05), indicating the variances are different among the three network structures. The mean and variance of % of cooperation in the scale-free network are the largest. Through the Kruskal–Wallis H test, we find the p-value is 0.00 (<0.05) and conclude that the results from the three network structures under Scenario 1 are different. Similarly, for Scenarios 2–7 we conduct simulation and perform statistical analyses. The results are summarized in Table 4, which shows the mean and variance of % of cooperation (column #5), % of path strategies adopted (column #6), and p-values for means, variances, and Kruskal–Wallis H distribution tests (column #7). We find that the dominant path strategies (column #6, top three, boldfaced) are different under different scenarios and network structures.

Table 3 Default settings of the parameters in the experimental system. No.

Parameters

Description

Default

1 2 3 4 5 6 7 8

Num-nodes rewiring probability connection probability theoretical unit initial strategy b c d

Number of nodes in the network Reconnecting probability in small-world network Connecting probability in a random network Whether to apply P⁄ in eq. (5) to the network Percentage of initial cooperation value of b in Table 1 value of c in Table 1 value of d in Table 1

80 0.2 0.02 True 0.5 6 10 4

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G. Jiang et al. / Information Sciences xxx (2014) xxx–xxx

(a) % of cooperation & defection in small world network

(b) path strategies in small world network

(c) % of cooperation and defection in random network

(d) path strategies in random network

(e) % of cooperation and defection in scale-free network

(f) path strategies in scale-free network

9

Fig. 3. % of cooperation and number of path strategies under three network structures in Scenario 1 (b < c, c > 2d).

Except for Scenarios 3 and 6, the variances under the scale-free structure are the largest, indicating that the game strategy the agent employs is very unstable (volatile) in the scale-free network, as it has a highly asymmetric connection among nodes. The larger variances a game strategy has, the more likely the group will have the Tit-for-Tat (retaliation) issue in the knowledge sharing game, as evidenced in Scenario 4. When cooperation strategy is dominant, the mean % of cooperation under scale-free network is the smallest, as seen in Scenarios 3, 4, 5 and 7. On the contrary, when defection is dominant, the mean % of cooperation under scale-free network is the largest, as shown in Scenario 1.

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Table 4 Statistical results of simulation data. Scenario

Expression

Parameters

Network type

Dominate strategy(mean, variance of % of cooperation)

% Path strategy (CDC, DDD, CDD, DCD, CCD, CCC, DCC, DDC)

p-Value (p1, p2, p3)

1

b < c, c > 2d

b = 6, c = 10, d=4

Small world random Scale-free

Defection(34, 6.17)

27.3, 0, 34.1, 0, 22.7, 15.9, 0, 0

0.00, 0.00, 0.00

Defection(34.37, 5.66) Defection(41.79, 7.08)

23.1, 0, 37.5, 0, 20.1, 19.3, 0, 0 25.9, 0, 45.1, 0, 12.8, 16.2, 0, 0

b = 6, c = 6, d=2

Small world random Scale-free

Defection(36.731, 4.88)

0, 10.4, 0, 45.6, 0, 0, 20.8, 23.2

Cooperation(52.8, 4.14) Same(49.2, 5.77)

0, 23.8, 0, 39.5, 0, 0, 20.5, 16.2 0, 25.7, 0, 33, 0, 0, 32.7, 8.6

Small world random Scale-free

Cooperation(87.5, 7.06)

2.8, 2.3, 5.3, 1.2, 5.2, 47, 32.7, 3.5

Cooperation(89.55, 7.4) Cooperation(59.6, 2.19)

1.8, 2.8, 1.9, 2, 12.8, 56, 18, 4.7 10.9, 11.4, 8.5, 11.4, 17.8, 12.2, 16.6, 11.2

Smallworld random Scale-free

Cooperation(87.79, 3.36)

7.1, 0, 1.1, 0, 38.1, 53.7, 0, 0

Cooperation(79.55, 2.94) Cooperation(72.44, 13.38)

9, 0, 4.2, 0, 43.1, 43.7, 0, 0 45, 0, 2.6, 0, 12.8, 39.6, 0, 0

Cooperation(98.7, 8.52)

0, 0.3, 0, 0.2, 0, 0, 98.4, 1.1

Cooperation(87.99, 7.38) Cooperation(82.43, 8.57)

0, 1.8, 0, 1.5, 0, 0, 77.6, 19.1 0, 0.5, 0, 4, 0, 0, 66.7, 28.8

Small world random

Cooperation(81.67, 2.98)

Scale-free

Cooperation(74.1, 6.98)

6.8, 0.2, 0.3, 5.4, 24.4, 32.1, 18.4, 12.4 12, 0.4, 3.2, 8.4, 10.3, 33.8, 13.7, 18.2 6.7, 0.2, 0.3, 5.4, 24.4, 32.1, 18.5, 12.4

2

3&6

4

5

7

b = c, b  c/2  d > 0

b < c < 2d

(b  c) = (b  c/2  d), b  c/2  d > 0

b  c/2  d > 0 b > c, c < 2d

b > c > 2d

b = 4, c = 6, d=5

b = 6, c = 4, d=2

b = 7, c = 6, d=5

b = 10, c = 6, d = 2

Small world random Scale-free

Cooperation(75.8, 4.38)

0.0, 0.06, 0.00

0.00, 0.00, 0.00

0.00, 0.00, 0.00

0.00, 0.00, 0.00

0.00, 0.00, 0.00

Note: p1 is value from ANOVA, p2 is value from variance homogeneity test, and p3 is value from non-parametric test.

When b equals c, the probability of choosing either a defection or cooperation strategy is 0.5. But the punishment parameter d in game payoff can impact the evolution of game strategy. Despite b = c, in Table 4 we find that the dominant strategies and path strategies under Scenario 2 are very different in each of the three networks. Defection is a dominant strategy in the small world network, while cooperation is a dominant strategy in the random network. But no dominant strategy exists in the scale-free network, in which the mean % of cooperation is about the same as the % defection (the probability is approximately 0.5 each). This suggests that in addition to parameters b, c and d, network structures may also impact the evolution of game strategy. Moreover, in Section 3.2 we use the dynamic replication method to prove that the initial % of cooperation (P0) impacts game equilibriums in Scenarios 3 and 6. Through simulation, we conduct tests to empirically examine the effect of P0 on the equilibrium of game strategy. Following the conditions of Scenarios 3 and 6 (i.e. b < c < 2d), we assume b = 4, c = 6, d = 5, which results in P⁄ = 0.5. When P0 = 0.3 (P0 < P⁄, corresponding to Scenario 3), we find the dominant strategy is cooperation under each of the three network structures. This result contradicts Proposition 1, as which is a macro level of analysis and does not consider the specific type of network structure. On the other hand, when P0 = 0.8 (P0 > P⁄, corresponding to Scenario 6), we find the dominant strategy is cooperation under each of the three network structures. This is consistent with Proposition 1. 5.3. Comparison of the experimental results under different game setting scenarios Table 4 shows that different scenarios (parameter settings) have different % of cooperation under different network structures. Through ANOVA and the nonparametric test we obtain Table 5, in which the ANOVA tests reveal that the averages % of cooperation among different scenarios are significantly different. Similarly, the homogeneity tests show that the variances

Table 5 Test results under different scenarios in different network structure (at a 95% confidence level). Network structure

p-Value of ANOVA

p-Value of variance homogeneity test

p-Value of nonparametric tests

Small-world network Random network Scale-free network

0.00 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.03

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G. Jiang et al. / Information Sciences xxx (2014) xxx–xxx Table 6 Test results under different initial cooperation percentage (at a 95% confidence level). Network structure

Initial percentage

Mean and variance of % of cooperation

p-Value of ANOVA

p-Value of variance homogeneity test

p-Value of nonparametric tests

Small-world network

0.3 0.5 0.8

94.57, 5.9 87.5, 7.05 96.06, 8.08

0.00

0.01

0.00

Random network

0.3 0.5 0.8

73.69, 12.3 89.55, 7.4 74.27, 5.49

0.00

0.016

0.00

Scale-free network

0.3 0.5 0.8

58.49, 2.15 59.6, 2.18 60.74, 3.59

0.00

0.00

0.03

Table 7 Test results at different levels of information noise (at a 95% confidence level). Network structure

K

Mean and variance of % of cooperation

p-Value of ANOVA

p-Value of variance homogeneity test

p-Value of nonparametric tests

Small-world network

0 1000 10,000

81.67, 2.98 75.80, 4.38 74.10, 6.98

0.00

0.056

0.00

Random network

0 1000 10,000

79.72, 3.76 74.87, 3.94 72.76, 7.84

0.00

0.00

0.00

Scale-free network

0 1000 10,000

82.24, 4.90 79.58, 3.97 72.31, 7.02

0.04

0.00

0.009

under the six scenarios are different in each network structure. We check the distribution differences of % of cooperation between groups through the nonparametric test (the Kruskal–Wallis H test), which uses ranks to determine if the samples are from different distributions. We find that they differ in different scenarios. In summary, different parameter settings, corresponding to different scenarios in the social commerce, have significant influences on the % of cooperation. 5.4. Experimental results under different initial % of cooperation setting We now test the impact of initial % of cooperation on overall % of cooperation. The initial percentages are set at 0.3, 0.5, and 0.8 respectively. The results are summarized in Table 6, from which we can conclude that the initial percentages of cooperation have significant influences on % of cooperation. From the study, we also find different initial cooperation percentages converge at different speed. An optimal initial setup percentage could steer the network to reach equilibrium rapidly. 5.5. Experimental result with incomplete information We now examine the impact of information noise on the % of cooperation. The information noise levels are set at k=0, 1000, and 10,000 respectively. We summarize the results in Table 7, which concludes that different information noises have significant influences on the % of cooperation connections, except for the homogeneity test of variances under the smallworld network. In fact, the mean value for k = 0, k = 1000, and k = 10,000 under the Small-world network are 81.67, 79.72, 84.24 respectively, and its variances are 2.98, 3.76, and 4.9, respectively. The greater the information noise is, the higher the variance of % of cooperation, and the larger the fluctuation in its % of cooperation over time. 6. Results and discussion In this research, we study the evolutionary equilibrium of knowledge sharing among social commerce users through the dynamic replication method. We analyze the behaviors of cooperation and defection in knowledge sharing among users in the virtual community and the evolutionary process of strategy choice by using the agent-based computational approach. We find different game setups (scenarios) has a significant influence on users’ choice of path strategy and the cooperation evolution of network. An efficient design of game payoff (penalty mechanisms d) can effectively regulate user behavior and increase the % of cooperation in group game. We found that different scenarios have different % of cooperation in evolutionary Please cite this article in press as: G. Jiang et al., Evolution of knowledge sharing behavior in social commerce: An agent-based computational approach, Inform. Sci. (2014), http://dx.doi.org/10.1016/j.ins.2014.03.051

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G. Jiang et al. / Information Sciences xxx (2014) xxx–xxx

equilibrium and different converging speeds in reaching the equilibrium. A favorable mechanism can effectively regulate and promote the knowledge sharing behavior among users in the virtual community. Network structures have a significant effect on the evolution of group cooperation and choice of path strategy. The % of cooperation and the evolution of strategy combination vary with the network structures. Although cooperation or defection may be a dominant strategy in a given scenario, the % of cooperation often varies significantly under different network types. Therefore, different reward and penalty measures should be adopted to guide the cooperation under different network structures, instead of taking up the same measure for all groups, i.e. communities of different network structure should adopt different strategies. From the experimental data, we find that the mean % of cooperation under scale-free network is the smallest when the cooperation strategy is dominant. On the contrary, the mean % of cooperation under scale-free network is the largest when defection is dominant. Therefore, except for setting optimal game parameters, managers should also pay attention to the impact of network structures on cooperation behavior. Possible effective strategies include applying positive guidance or negative impedance on key nodes or paths. The initial cooperation ratio (P0) has a significant influence on the evolution of % of cooperation and choice of the path strategy. We also find different P0 will reach equilibrium at different speed. A good initial percentage would steer the group game to arrive at equilibrium rapidly. The information noise has a significant influence on the cooperation of knowledge sharing. The greater the information noise, the higher the variance of % cooperation, and the larger the fluctuation of evolutionary curve over time. This study employs agent-based simulation method to explore the evolution of knowledge sharing behavior in social commerce. It contributes to the literature in twofold: (1) Many studies have examined the motive of knowledge sharing in virtual communities, but few have focused on the motive of continuous use and behavioral evolution. We develop a dynamic replication model for knowledge sharing among users in the virtual community from the perspective of evolutionary game, and the model can be used to analyze the macro-level of group game. (2) We design a computational model that integrates agent, evolutionary game, and social network. The model can help visualize the evolution of % of cooperation, defection and path strategy; grasp the dynamic evolution features in knowledge sharing game over time; and explore micro-level interactions among users in different networks under various scenarios. Four important managerial implications can be drawn for social commerce management: (1) Different virtual communities (with different network structures) should adopt different macro-level managerial strategies, i.e. customize the reward and penalty mechanisms. Different incentives and penalties can influence user’s choice of strategies and affect the performance of knowledge sharing. (2) Managers should pay close attention to the initial motive of users, i.e. whether users are willing to cooperatively share knowledge or not. An agent’s initial decision will affect the knowledge sharing behaviors of others and the entire community. Assessing and understanding the motivations of users are crucial. (3) Intervention strategies should be applied to the virtual community when necessary. The forum moderator or management should explain the policy regularly and guide the learning of knowledge with facts. For example, management can provide objective data, graphics, direct quotes or video; place authoritative and highly reliable posts on top; gradually carry out the evaluation and survey on the credibility of historical reports and the trustworthiness of user posts; and properly reveal any relevant information. These methods will promote knowledge learning and give constraints to key paths and nodes in the network. Typical examples include cutting off the communication of a few users, closing some information of other users, and limiting the activities of users with poor credibility records. (4) Providing flawless channels for interactions will facilitate knowledge sharing and remove communication obstacles among users. Also, one can add popular auxiliary devices to enhance the communication. For example, integrating social media tools, such as Twitter, Alitalk, QQ, and blogs into the virtual community, will allow users to conveniently and quickly interact with each other in the forum. This paper has some limitations. First, we assume the network structure is fixed, and we did not consider the evolution of the network structure. However, the virtual community may dynamically change over time: some nodes may become dormant, while other nodes may enter or even exit the network. Second, our study did not consider the personality differences in individual users, e.g. trust, intimacy, and alienations. Third, the effects of different guides or impedances on key nodes and paths are not analyzed. We shall add these elements into our future research, and offer theoretical foundation for dynamic behavior evolution of knowledge sharing, as well as decision-making support for managerial practice. 7. Conclusions The virtual community is an growing phenomenon of e-commerce. Designing effective managerial measures in the ecommerce social community can facilitate knowledge sharing among users, promote e-commerce activities, and improve e-business performance. This study examines the evolution of knowledge sharing behavior in social commerce based on the dynamic replication method and agent-based computational approach, and draw conclusions that help managerial practice. In comparison with other methods, the proposed methods offer valuable macro- and micro-level insights on evolution of knowledge sharing in social commerce. We find that the rules (e.g. those stipulated by ebay community) of knowledge Please cite this article in press as: G. Jiang et al., Evolution of knowledge sharing behavior in social commerce: An agent-based computational approach, Inform. Sci. (2014), http://dx.doi.org/10.1016/j.ins.2014.03.051

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G. Jiang et al. / Information Sciences xxx (2014) xxx–xxx

sharing game and social network structure significantly affect the degree of cooperation and knowledge sharing among users. The greater the noise information is in the network, the less stable the users’ behavior will be. An optimal ratio of initial cooperation can facilitate cooperation and help the system reach equilibrium state quickly. The dynamic replication method can analyze macro-level evolutionary trend and approximate the equilibrium for group game. On the other hand, the multi-agent simulation system for group game can visualize the interactions among users at micro-level, and present macro-level insights about group behavior in the end. The findings derived from the macro- and the micro-level can help managers attain evolutionary data in different game settings and network structures. These data can aid mangers in designing the best knowledge sharing mechanism and regulating the dynamic game environment. Agent-based models have proven to be useful for understanding business dynamics. The advanced agent based computational approach integrates both the agent-based model and the multidisciplinary models. The advanced agent-based computational approach integrates both the agent-based model and the multidisciplinary models. By combining the methodologies in economics, social studies, and management, the proposed method bridges the gap between multiple fields, and offers a valuable tool for researchers to conduct interdisciplinary studies. Acknowledgements We thank the editor-in-chief, the associate editor, two anonymous reviewers for their valuable comments and suggestions on this work. This work was partially supported by a grant from the National Natural Science Foundation of China (Nos. 71101047 and 70833005), China Postdoctoral Science Foundation (Nos. 2011M500119 and 2012T50674), and S&T project of Hubei Provincial Department of Education (No. D20132201). Appendix A A.1. Proof of Proposition 1 We take dP as the y axis and P as the x axis. In view of the distribution features of stable equilibrium points in Eq. (4), dt Figs. A1 and A2 correspond to the conditions when P⁄ > 1 and P⁄ = 1, respectively. In Fig. A1, there are two stable equilibrium

dP/dt

0

1 P*

P

Fig. A1. P⁄ > 1 (scenario 1).

dP/dt

0

1

P

P*

Fig. A2. P⁄ = 1 (scenario 1).

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G. Jiang et al. / Information Sciences xxx (2014) xxx–xxx

dP/dt

0

1

P

P*

Fig. A3. P⁄ = 0 (scenario 2).

dP/dt

0 P

1

P

*

Fig. A4. P⁄ < 0 (scenario 2).

dP/dt

0

P*

1

P

Fig. A5. 0 < P⁄ < 1 and P0 < P⁄ (scenario 3).

dP/dt

0

P 1

P*

Fig. A6. P⁄ > 1 (scenario 4).

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G. Jiang et al. / Information Sciences xxx (2014) xxx–xxx

dP/dt

P*

0

P

1

Fig. A7. P⁄ = 1 (scenario 4).

dP/dt

0 P*

P 1

Fig. A8. P⁄ = 0 (scenario 5).

dP/dt

P*

0

1

P

Fig. A9. P⁄ < 0 (scenario 5).

dP/dt

0

P*

1

P

Fig. A10. 0 < P⁄ < 1 and P0 > P⁄ (scenario 6).

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G. Jiang et al. / Information Sciences xxx (2014) xxx–xxx

dP/dt

0

P*

1

P

Fig. A11. 0 < P⁄ < 1 (scenario 7).

points at P = 0 and P = P⁄. However, the initial values of the system are always within [1]. As P⁄ (>1) cannot be chosen as a stable equilibrium point, only P = 0 is chosen as the stable equilibrium point. That is, all are defections. As to Fig. 2, apparently only P = 0 appears at the stable equilibrium point. Under Scenario 2, the stable equilibrium points are distributed as in Figs. A3 and A4. Similarly, the stable equilibrium point appears at P = 0. Under Scenario 3, the corresponding stable equilibrium points are as shown in Fig. A5. Two stable equilibrium points may appear at P = 0 and P = 1. The choice of the values depends on the initial value of the system. If the initial value P0 < P⁄, then the stable equilibrium point is at P = 0. When P 0 P P ; it is at P = 1. Therefore, under Scenario 3, the group evolutionary equilibrium will reach ‘‘defection’’. A.2. Proof of Proposition 2 Under Scenario 4, Figs. A6 and A7 correspond to conditions when P⁄ > 1 and P⁄ = 1, respectively. Apparently, the stable equilibrium point only appears at P = 1. Under Scenario 5, the stable equilibrium point corresponding to P⁄ = 0, P⁄ < 0 is shown in Figs. A8 and A9. In Fig. A8, the stable equilibrium point only appears at P = 1. In Fig. A9, there are two equilibrium points shown respectively at P = P⁄, P = 1. However the initial value of the system only falls within [0, 1]. Thus, the stable equilibrium point can only appear at P = 1. Under Scenario 6, the corresponding stable equilibrium points are shown in Fig. A10. Two stable equilibrium points appear at P = 0 and P = 1 respectively. The equilibrium value depends on the initial value of the system. If the initial value P0 < P⁄, then the stable equilibrium point is at P = 0. When P0 P P  , it is at P = 1. Therefore, under Scenario 6 the group evolutionary equilibrium will reach ‘‘cooperation’’. A.3. Proof of Proposition 3 Fig. A11 illustrates the results under Scenario 7. Apparently, the only stable equilibrium point under Scenario 7 is at P = P⁄. References [1] S.J. Yu, The dynamic competitive recommendation algorithm in social network services, Inf. Sci. 187 (2012) 1–14. [2] C. Shi, Social Media have Higher Impact on Online shopping of Chinese Citizens, 2012. (accessed: 10.03.13). [3] Y.-M. Li, H.-W. Hsiao, Y.-L. Lee, Recommending social network applications via social filtering mechanisms, Inf. Sci. 239 (2013) 18–30. [4] J.-F. Wang, E-commerce communities as knowledge bases for firms, Electron. Commer. Res. Appl. 9 (2010) 335–345. [5] W. He, K.-K. Wei, What drives continued knowledge sharing? An investigation of knowledge-contribution and -seeking beliefs, Decis. Support Syst. 46 (2009) 826–838. [6] Y. Sun, Y. Fang, K.H. Lim, Understanding sustained participation in transactional virtual communities, Decis. Support Syst. 53 (2012) 12–22. [7] C. Romm, N. Pliskin, R. Clarke, Virtual communities and society: toward an integrative three phase model, Int. J. Inf. Manage. 17 (1997) 261–270. [8] J. Preece, Online Communities: Designing Usability and Supporting Sociability, Wiley, New York, 2000. [9] A. Bhattacherjee, Understanding information systems continuance: an expectation–confirmation model, MIS Quart. 25 (2001) 351–370. [10] R.M. Ryan, E.L. Deci, Intrinsic and extrinsic motivations: classic definitions and new directions, Contemp. Educ. Psychol. 25 (2000) 54–67. [11] C.-M. Chiu, M.-H. Hsu, E.T.G. Wang, Understanding knowledge sharing in virtual communities: AN integration of social capital and social cognitive theories, Decis. Support Syst. 42 (2006) 1872–1888. [12] M.-H. Hsu, T.L. Ju, C.-H. Yen, C.-M. Chang, Knowledge sharing behavior in virtual communities: the relationship between trust, self-efficacy, and outcome expectations, Int. J. Hum. Comput. Stud. 65 (2007) 153–169. [13] D.-N. Chen, T.-P. Liang, Knowledge evolution strategies and organizational performance: a strategic fit analysis, Electron. Commerce Res. Appl. 10 (2011) 75–84. [14] U. Lechner, J. Hummel, Business models and system architectures of virtual communities: from a sociological phenomenon to peer-to-peer architectures, Int. J. Electron. Commerce 6 (2002) 41–53.

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