Chapter 2. Theoretical Background on Network Formation Models
2.3. Complex Adaptive System Approach
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openness, so it may be difficult to define system boundaries
a history whereby the past helps to shape present behavior
elements in the system are not aware of the behavior of the system as a whole and respond only to what is available or known locally.
In comparison to stochastic modeling and strategic network formation models, the Complex Adaptive Systems approach characterizes the following concepts: (1) System (2) Adaptivity and (3) Complexity. A System is a representation of individual entities interacting with each other. An entity in a system is characterized by its state, its transition rules, its behavior and finally a context within which the entity is presented. A system evolves in time due to the local state transition (local state changes) of its individual entities. Adaptivity implies that the system is both flexible and robust and it shows the capability of a system or its entities to perform tuning behavior in contingent situations.
Such systems are open and situated, which are important driving force for complexity. As we can see, the Complex Adaptive Systems approach helps the system modeler in investigating both the characteristics of individual entities at the micro level and their interacting forces at the meso and macro levels. In addition to that it considers the feedbacks in interactions during the system analysis. That is why it can be considered as a hybrid approach.
Examples of complex adaptive systems may include the healthcare organizations(Rouse 2008, McDaniel, Driebe et al. 2013), communities, political parties, the brain (Morowitz and Singer 1995), the immune system (Ahmed and Hashish 2006), the stock market (Mauboussin 2002), the ecosystem (Levin 1998, Levin, Xepapadeas et al. 2013), and any human social group endeavor (Eidelson 1997). However, some might argue that not all of these things share every characteristic of complex adaptive systems.
33 Out of the empirical studies investigated within the scan, few of the systems neatly or unquestioningly corresponded to all of the properties of complex adaptive systems.
Despite mentioned characteristics of complex adaptive systems above, socio- economic complex adaptive networks have several interesting features that distinguish them from general classes of complex adaptive systems (CAS). Therefore, study of network dynamics among agents requires the additional of a whole new sets of parameters to our network growth models. For example, an economic model exists within the diverse economic elements of socio-economic complex adaptive networks and basic psychological biases also cause major deviations from rational behavior. Therefore, it is not a safe to assume that agents follow the same pattern of behaviors. In such networks due to the path dependency among the elements of the system, we are able to observe inflexibility and mal adaptiveness in the structure. Finally, the evolutionary process that such a system experiences can only be understood in an explicit historical time dimension.
Therefore, in this thesis we argue that understanding, designing, and managing socio- economic complex adaptive networks require an in-depth understanding of the economic behaviors of their agents as well as the social system, within which the arrangement of social interactions of their agents are identified.
Table 2.2 summarizes different views on the network formation models (stochastic vs strategic network formation models), and it compares them with respect to main characteristics of the proposed approach for studying socio-economic complex adaptive networks. As we can see, lack of having a proper economic incentive modeling is obvious within stochastic network formation models. We assume that Scale-free model (Barabási, Albert et al. 1999, Albert and Barabási 2002) is the only stochastic network formation model in the literature that slightly point to this economic incentive modeling
34 feature, it is not mentioned explicitly in the literature though. Our assumption is based on the specific network growth model of a Scale-free network. It consider the probability of link establishment to be related to cumulative degree distribution of the nodes within the network. Therefore, we think having such a preference for connecting to high degree nodes (actor’s centrality) can be a sort of economic incentive modeling. Time has a certain role in the evolution of such networks and as time goes by network evolution impacts individuals’ future choices. Having said that is it difficult to make such an assumption for other network models in this category (i.e., small-world or random network). Strategic network formation models do not have such limitations, they are perfectly designed to target an economic feature among network actors. Utility maximization for example, can be considered as a sort of an economic incentive for the process of link establishment.
What is missing in strategic network formation in fact is the lowest flexibility in modeling heterogeneity. Usually such models assume that all the individuals follow the same behavior or the same economic model as others. Following our line of arguments, we believe that a complex adaptive system approach would tackle limitations of both stochastic and strategic network formation models.
In this thesis, we consider the clustering coefficient and average path length as the emerging characteristics of a socio-economic complex adaptive network. We aim to capture and explain the changes in those emerging characteristics as the agents in the system interact in not apparently random ways but with a proper incentive modeling. Out of all those interactions final network characteristics emerge which ultimately determine the outcome of the individuals as well as the whole system. Consequently, change in the behavior of the agents happen and will be feedback to the system itself.
35 In the following chapters we first highlight the importance and necessity of capturing the economic incentives among component of the socio-economic complex adaptive system, as well as the importance of connectivity pattern among the elements of such system. Our focus is on human-to-human communication environments, where the process of network growth requires an economic inventive and the process of link establishment among network members are not random. We consider them strategic responses towards what others are doing within the network. We also discuss the applicability and necessity of applying a hybrid approach in the theory of network formations. Finally, we show how the emergence of certain network characteristic affect the outcome of the individuals (i.e., learning outcome or utility gain at the individual level) within socio-economic complex adaptive networks .
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Approach Category Model Incentive Modeling Preference Heterogeneity Nonlinear
Interactions
Feedback Loops
Presence of a History
Imperfect Knowledge
(Bounded Rationality)
Strategic Responses of
Actors
Structuralism Approach
Stochastic Network Formation Model
Erdős-Renyi 1959
Random graph model × Random × × × × ×
Watts-Strogatz 1998 Small-World model
× Actor’s Centrality × × × × ×
Barabási–Albert 1999 Scale-Free model
Node Structural Importance
Actor’s Centrality × ×
Individualism Approach
Strategic Network Formation Model
Jackson 1996, Symmetric connection model & Co-author model
Economic
Incentive Modeling Utility Maximization × × × ×
Konig et al 2009 Economic
Incentive Modeling
Actor’s Centrality × × ×
Buechel 2009 Node
Structural Importance
Actor’s Centrality × × ×
Strategic complement &
Strategic substitute Threshold based
complementing or
substituting others × ×
Combination of Structuralism &
Individualism Approach
Complex Adaptive System approach
Proposed Interaction Model in chapter 5 (Koohborfardhaghighi and
Altmann 2016a)
Economic Incentive Modeling
Utility Maximization
Table 2.2: Different views on the network formation models and their comparisons.
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