2009年12月10日 星期四

NETWORK STRUCTURE, STRUCTURAL EQUIVALENCE

NETWORK STRUCTURE, STRUCTURAL EQUIVALENCE AND GROUP PERFORMANCE: A SIMULATION RESEARCH ON KNOWLEDGE PROCESS
HUA ZHANG
School of Management, Xi’an Jiaotong University, 28 Xianning West Road,
Xi’an, 710049, China
E-mail:zhang_hua@live.cn
YOUMIN XI
Xi’an Jiaotong-Liverpool University
Suzhou, 215123, China y
E-mail: ymxi@xjtu.edu.cn
According to the trade-off between information diffusion and diversity in an efficient network, we extend Lazer’s simulation model on parallel problem solving by adding partner selection strategy: structurally equivalent imitation. In this way we can examine how the interaction of network structure with agent behavior affects the knowledge process and finally influence group performance. Our simulation experiment suggests that when agents adopt structure equivalence imitation the whole organization implicitly would be divided into independent sub-groups which converge on the different performance level and lead the whole group to a lower performance level.
Keyword: network structure, structural equivalence, agent behavior, group performance
1. Introduction
According to the different definition on social capital, there is still controversy over the optimal structure of that over the relative benefits of brokerage network and cohesive network structure. The former refers to a particular network which occupies the sole intermediate position between others who are disconnected and can interact only through the broker; the latter refers to the situation in which all the members are connected each other. Proponents of brokerage argue for the benefits of unique information which is the valuable resource of innovation; proponents of cohesive network argue for the benefits of efficient information diffusion and normal trust which promotes cooperation (Coleman 1988; Burt 2004).
Research on this social capital debate has often focused on these two types of network affects without considering the network content. Next to structure, the network literature has recently showed increased attention for the influence of the content conveyed through ties on resource acquisition (Rodan et al 2004; Fleming et al 2007) and the individual’s strategic orientation (Obstfeld 2005).
Prior studies highly illuminate the passive role of network in adjusting the knowledge process in organization but neglect the active role that individual can play in keeping individual heterogeneity and linking to the different others. Without considering network content variables some plausible conclusions deduced from the above studies would be argued: dose diversity can always lead to a high performance level? How the interaction of network structure with agent behavior affects group performance? To address these questions and extend what has been, until now, peripheral attention to actor’s behavior strategy in exploration-exploitation literature. This paper focuses on the individual behavior, beginning with the assumption that advice network structure is a factor but not the only factor accounting for knowledge process. We contribute to a greater clarity and better understanding of how agent’s partner selection affects the knowledge process and finally lead to different performance level. By considering the agent’s behavior we can also explore how the interaction of network with agent behavior affects the group performance.
2. Literature review and concept model
Inherent to the social capital debate is a paradoxical trade-off between cohesive networks promoting cooperation and information diffusion efficiency and sparse networks flexible to heterogeneous knowledge and ideas. Since we cannot simultaneously maximize both facets of a network, this reflects a sharp trade-off between information diffusion and diversity in an efficient network (figure 1).



Figure 1: The trade-off between information diffusion and diversity in an efficient network.
Source: Lazer, David; Friedman, Allan. Administrative Science Quarterly. 2007

In recent years the role of network content and its interaction effect with network structure has emerged as an important area of inquiry in our understanding of innovation and group performance. It is well recognized that network content variable including the attribute of actors and actors’ behavior pattern complement network structure to promote creativity and innovation on the one hand and cooperation and coordination on the other. According to their surrey research, Rodan (2004) proposed that, while network structure matters, access to heterogeneous knowledge is of equal importance for overall managerial performance and of greater importance for innovation performance. Developing a social definition of creative success and tracing the development of creative ideas, Fleming propose that interaction of structure with the personal attributes affects the brokerage on generating the initial insight and future idea development (Fleming et al 2007). Obstfeld introduced tertius iungens strategic orientation and propose that this orientation with dense social networks and diverse social knowledge predict individual involvement in innovation (Obstfeld 2005).
While prior work has demonstrated a relationship between network structure and group performance, inadequate attention has been paid to network content (Rodan, S etl, 2004). Our study draws on both structural and content perspectives in examining the way network structure affects knowledge process which contributes to group performance. Particularly, we focus on actor’s partner selection. Contrasting to the ‘know how’ and ‘know what’ knowledge, ‘know who’ reflects another emergent important kind of knowledge in organization learning (Borgatti and Cross 2003). By considering the agent’s partner selection behavior in inquiring information in their advice network, we can examine how the interaction of network structure with agent behavior affects knowledge process (figure 2).
Previous simulation research on agents’ communication design almost paid all their attention on agents’ neighbors (Hanaki et al 2007; David and Friedman 2007). That is, agents could only communicate with those who are directly connected with them. Although this nearby imitation pattern reflects agent’s some kind of geography proximity, but this design leads to some plausible conclusions. Such as in Lazer’s study, when agents only consider emulating their direct neighbors, regardless of what the network structure is, network density became the main factor affecting knowledge diffusion. Network topological structure is supposed to be an important role in information diffusion (Cowan 2004). We argue that different network structures would have different influence on coordinating exploration and exploitation even they may have the same density. Lazer.D also indicated that some different assumptions on emulate process could have significant effects on group performance (David and Friedman 2007).









Figure 2: concept model: how partner selection influence the relationship between network structure and knowledge process
Following the preceding discussion on the potential risks of ignoring actor’s other imitation behavior, rather than assuming agent emulate the directly connected neighbors, we assume that agents will pay more attention on those who are structurally equivalent. Loosely speaking, structural equivalence refer to the extent to which two nodes are connected to the same others (Stanley and Katherine 1994). The fact that two agents are structurally equivalent indicates that they may have the same social position, same role or even completely substitutable. Based on the similarity theory agent are more likely to do the same thing as those who are similar with themselves. Structural equivalence also grasps agents’ myopia perfectly. Because of myopia agents are unable to directly evaluate all the potential solutions in the whole organization, besides emulating the directly connected people, imitation pattern of structurally equivalent is another heuristic partner selection rule when agent faces complexity problem.
Drawing on the discussion above it is very reasonable to assume that structurally equivalent people are the favorite targets of imitation.
3. The model
3.1. Problem space and NK model
In this paper we extend Lazer’s simulation model on parallel problem solving by adding the partner selection rules. The concept of parallel problem solving is first proposed in Lazer’s study, which portrays a context where all the agents are engage in the same problem solving and the success of any one or subset of agents has no direct effect on other agents (David and Friedman 2007). NK model was used to portray this parallel problem solving. In NK model, K controls the degree of independence among decisions which ranges from 0 to N-1. Different values of K represent different extent in complexity of problem space (figure 3).


Figure 3: problem spaces represented by NK model.
Source: Lazer, David; Friedman, Allan. Administrative Science Quarterly. 2007
3.2. Partner selection
We assume that agent is myopic, unable to detect the best solution in group. Furthermore, there is also lacking incentive for agents to public their solutions. To improve their performance and explore at a higher level in the future agents have to interact with other agents and mimic the most successful one among the available candidates.
Besides the most adopted agent’s communication pattern ---near neighbor selection we introduce another heuristic partner selection rule: structurally equivalent selection. In our model agents tend to emulate those who are structurally equivalent with them. The two agents are supposed to be exactly structurally equivalent if they have the same relationship to all other agents (Stanley and Katherine 1994). Pure structural equivalence can be quite rare in social relations but approximations to it may not be so rare. In network structure analysis researchers often are interested in the examining the degree of structural equivalence. There are many ways in which agents could be defined as approximate structural equivalence. And some algorithms have been particularly useful in applying graph theory to define the structural equivalence, such as “Euclidean Distance”, “Correlation” (Stanley and Katherine 1994). Actually there are indeed a very large number of the algorithms we can use to examine group sets of agents into categories based on some commonality in their positions in network. For the sake of simplicity, we here only consider a relaxed criterion: agents will fall into the same class if they have the same sum of out-degree and in-degree. This criterion relaxes the conditions of the same agents actor connects to/with. Rather than connecting to the same agents, only the sum of degrees represent for structural equivalence.
3.3. Network structure
Our imitation pattern of structural equivalence is defined by the sum of a node’s degree. In this case, not only network density but also network structure will affect system-level performance differently. To explore the influence of structurally equivalent imitation on system performance, we employ a regular network and an asymmetry network. The former is represented by a fixed grid to represent the advice network in which everyone has the constant number of connectors (we will call this network RU for short) and the other is a preferentially attached network (we will call this network PA for short). In a RU network, each individual is assumed to be connected by its fixed number neighbors on either side of it (see figure 4, in this paper each person has 4 neighbors).


Figure 4 preferentially attached network and regular network

We employ Jan’s algorithm to create a preferentially attached network which captures a “rich-get-richer” dynamic, by which nodes that already have many interactions are more likely to add a further interaction than the nodes that have few interactions (Jan and Nicolaj 2007). Notice that, to eliminate the effect of network density, we create these two kinds of networks with the same density.
4. Results and interpretation
The simulation experiment is conducted under the following conditions: we consider a organization of 50 agents. All the organization members are engaging in solving a problem including 10 decisions. That means, we assumed N=10, and K=4 for the NK model. When N=10, there are 1,024 possible solutions for each problem space. The initial solutions of the actors are randomly generated, and those 50 agents are randomly placed in their communication networks.
Figure 5 illustrates the effect of RU network and PA network on the equilibrium performance level when agents adopt the structurally equivalent imitation strategy. As shown in Figure 5 RU network quickly finds a good solution and outperforms PA network all the time. This result can be explained by their dramatically different topological structure.












Figure 5 The organization performance change with PA network and RU network under the condition of structurally equivalent imitation

All the agents are the structural equivalent in RU network while in PA network agents belong to a few structural sub-groups because of the structurally equivalent partner selection. That is, PA network is no longer a single-component network but RU network still does. This brings both positive and negative effect on performance: on the one hand, agents only search the best solutions in the sub-group they belong to, the existence of sub-group keeps the information diversity from the whole organization’s angle, which positively affects organization performance; on the other hand, there is no communication among agents belonging to different sub-group. Sub-groups in PA network are independent with each other. This structural obstacle cut off the information diffusion, which is negatively related to performance.













Figure6 the ratio of sub-group in organization with final performance

When agent chooses those who are structurally equivalent to emulate, the whole organization is partitioned to several independent sub-groups and agents belonging to different sub-groups have no opportunity to communicate each other at all. Just like the local search good solutions only spread in a close circle and can not diffuse over the whole organization. Structure equivalence keeps the diversity from the system-level angle at the mean time builds the bastions which stops good solutions diffusion. In this case, each sub-group will converge on different performance level. This result is captured in Figure 6, which plot the final performance level every sub-group achieved. Furthermore, Figure 6 also shows the ratio of the number of the sub-group over the whole organization, which suggests that large sub-groups can not necessarily lead to a high performance level. This result contradicts Kent’s research in which he propose that large organization have the advantage over small organization in coping with complexity (Kent et al 2006). Our experiment shows that sometimes large organization can not outperform small organization. Although these sub-groups keep diversity lack of communication among different structurally equivalent sub-group leads to a lower performance level the whole organization achieved.
5. Conclusion
According to the debate on the trade-off of information diffusion and diversity in a network, we add partner selection to the Lazer’s simulation model to examine how the partner selection affects knowledge process and finally influence group performance.
Previous studies assuming that agents emulate the directly connected people get to the conclusion that network density attribute to the final organization performance regardless of what topological structure of advice network is. In our extending model we assume another heuristic partner selection rule which agents choose to emulate their structurally equivalent peer, under the condition of this agent imitation strategy network topological structure (even with the same density) plays a significant role in knowledge flow and finally influence the group convergent performance level. Agent’s imitation pattern determines the direction of knowledge flow. When agents adopt the structurally equivalent imitation the whole organization no longer is a single-component network but can be seen as many independent sub-group. No communication among different sub-groups will lead the whole group to a lower performance level.
Our simulation study has much management implication for new product development team and R&D institution. In the situation of such an organization where all the engineers are solving the same complex problem which may has many plausible solutions, the challenge confronting to the manager is how to structure the advice network and induct engineers’ behavior to achieve a high performance level both in the short-run and long-run. Our simulation experiment suggests that both network configuration and actor behavior can be employed to achieve this goal.
Notice that when granting more freedom to organization members they may actually choose to emulate their structurally equivalent peers. Over time, people may lock in to a limited set of people with whom they are familiar with and frequently interact, which might be efficient but yield suboptimal solution if other people are better sources. Especially when the sub-group is small, our experiment has proved this point. Give the importance of people as critical sources of knowledge, our study indicate the needs to avoid people’s structurally equivalent imitation and other path dependence actions.
In this paper, we have considered only a very simple rule to judge the structural equivalence----the sum of the indegree and outdegree, and our design of imitation extent is equally simplistic, thus, many obvious extensions are easily conceivable.
6. Acknowledgments
We gratefully acknowledge the financial support from the National Nature Science Foundation of China under the grant number 70121001 & 70772109
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