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This paper deals with the issue of social networks evolution. The Schelling‘s social segregation model is applied to analyze the competition between social networks such as Facebook, Myspace and others. It is known that social networks sustain network externality. This means network can only grow, but recent data shows that Myspace is shrinking. The proposed model is explaining this paradox.
Keywords: social networks, network externality, segregation, Schelling‘s model, Myspace.
Due to rapid development of information technologies and the growth of social networks, the concepts of network externalities, network economy and network effects are often analyzed in the economic studies. First significant works in this area are made by Katz and Shapiro (1985), Farrell and Saloner (1985). Their research was extended later by Economides and Himmelberg (1995), Liebowitz and Margolis (1994). The presence of network externality causes the growth of consumer utility as the new users are joining the network. In the social network context this means that number of users is condemned to grow. But one of the first and biggest social network called Myspace is shrinking in recent years.
There are some studies in the scope of social networks. Skyrms and Pemantle (2000) present the dynamic model of social network formation. Model is based on individual agents who stochastically interacting. Boyd (2007) explores the social dynamics of mediated public life in social network sites. Other model offers a conceptualization of online social networks which takes the Web site into account as an actor, an initial exploration of the concept of a consumer–Web site relationship, and a conceptual model of the online interaction and information evaluation process (Brown, Broderick, & Lee, 2007).
There are some papers which concentrate on analyses of specific characteristics of social networks (Cheng, Dale, & Liu, 2007) (Juan-Antonio, Miller, & Wellman, 2008).
Szabo and Bernardo (2008) present a method for accurately predicting the long time popularity of online content from early measurements of user’s access.
Schelling (1969) (1971) analyzed racial segregation problems. He showed that a small preference for one's neighbors to be of the same color could lead to total segregation. He used coins on graph paper to demonstrate his theory by placing pennies and nickels in different patterns on the "board" and then moving them one by one if they were in an "unhappy" situation.
In this paper segregation model is applied to describe the competition of social networks. Suppose there are two social networks: A and B. The tolerance function of one network to the other is this:
Here mBA is coefficient of tolerance to the network B in the network A. It shows the ratio of B network members, which can be tolerated by the network A when the latter has nA members. Variables nA and nB are in interval [0..1]. For example, if mBA=3 then this means that A network tolerates three times bigger B network. Assume that where is this tolerance function:
It can be shown graphically as:
This picture displays members of network A toleration to the network B. For example, one fourth (0.25) of network A members can tolerate five time bigger number of users from network B. If number of members in network B increases, then it will be observed the flow of users from A to B. In case of mBA=0 only network A exists. If mBA=10 only network B exists, because no one wants to be in network A.
Presume networks A and B have the same tolerance function. Multiplying network A tolerance function by network A number of members it is obtained network response function. This network response function is similar to the reaction function between oligopolies. If we do the same with network B, we get this picture:
The vertically oriented parabola shows the part of members (nA) of network A which is static when number of members in network B is equal to nB. Figure 2 presents this response function nB=10nA-10*(nA)1.5. Arrows display the direction of dynamics. In case of dotted arrows only one network can exist. This reflects situation when one network expands very fast in comparison with the other in early stages. This means that first player has very big competitive advantage.
Non dotted arrows displays long term equilibrium where network A and network B both exists. This equilibrium depends on response functions of the networks and in other cases it can be very different.
In order to forecast the fate of social network Myspace one needs to calculate the tolerance function of Myspace to other social networks and vice versa. By plotting this data as response functions and establishing current position it is possible to determine the long term equilibrium.