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The application of segregation model in economics: social networks competition case

The application of segregation model in economics: social networks competition case
Petras Lickus, аспирант

Участник конференции

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:

 

mBA(nA)=f(nA).

(1)

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:

 

mBA=10-10*(nA)0.5.

(2)

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 (nAof 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.

References:

  1. Boyd, D. (2007). Social network sites: public, private, or what? Retrieved January 3, 2012, from http://en.scientificcommons.org/51838147
  2. Brown, J., Broderick, A. J., & Lee, N. (2007). Word of mouth communication within online communities: Conceptualizing the online social network. Journal of Interactive Marketing, Vol. 21, No. 3, pp. 2-20.
  3. Cheng, X., Dale, C., & Liu, J. (2007). Understanding the characteristics of internet short video sharing: Youtube as a case study. Quality of Service, 2008. IWQoS 2008. 16th International Workshop on, (pp. 229-238). Enschede.
  4. Economides, N., & Himmelberg, C. (1995). Critical mass and network size with application to the US fax market. Discussion Paper no. EC-95-11, Stern School of Business, N.Y.U.
  5. Farrell, J., & Saloner, G. (1985). Standardization, compatibility, and innovation. Rand journal of economics, Vol. 16, No. 1, pp. 70-83.
  6. Juan-Antonio, C., Miller, E., & Wellman, B. (2008). How Far and With Whom do People Socialize? Empirical Evidence about Distance Between Social Network Members. Transportation Research Record: Journal of the Transportation Research Board, No. 2076, pp. 114-122.
  7. Katz, M. L., & Shapiro, C. (1985). Network externalities, competition, and compatibility. American economic review, Vol. 8, No. 3, pp. 424-440.
  8. Liebowitz, S. J., & Margolis, S. E. (1994). Network externality: an uncommon tragedy. Journal of economic perspectives, Vol. 8, No. 2, pp. 133-150.
  9. Schelling, T. (1969). Models of segregation. The American Economic Review, Vol. 59 No. 2, pp. 488-493.
  10. Schelling, T. (1971). Dynamic Models of Segregation. Journal of Mathematical Sociology, Vol. 1, No. 2, pp. 143-186.
  11. Skyrms, B., & Pemantle, R. (2000). A Dynamic Model of Social Network Formation. Proceedings of the National Academy of Sciences of the United States of America, Vol. 97, No. 16, pp. 9340-9346.
  12. Szabo, G., & Huberman, B. (2008). Predicting the Popularity of Online Content. Retrieved December 28, 2011, from http://ssrn.com/abstract=1295610
Комментарии: 2

Turmanidze Tamila

In our opinion, one limitation faced by an incentive-based approach to modeling network formation is that many of the models that are analytically tractable end up with some limitations on their range. They can provide broad insights regarding things and they can help explain why one might see small worlds, and some other prominent characteristics of observed networks. However, many of the models are quite stark in their detail, and as a result end up with networks that are quite simple emerging as the stable and/or the client of networks. Networks like stars are quite special, and rarely observed in real social settings. While these can be thought of as analogs to hub-and-spoke sorts of networks, it is clear that the models are not so well suited in terms of trying to match the observed form of many large social networks, where there is a huge amount of heterogeneity in the network structures. There are two ways to deal with this. One is to work with simulations and agent-based modeling to introduce heterogeneity. Another is to bring in some randomness to the settings. Random network models have provided some simple models that end up providing insights into some observed networks. Such random models, however, end up being somewhat mechanical and new processes can be needed every time some difference in network structure is observed empirically. On the one hand the economic approach leans too heavily on choice and at the other extreme random network models lean too heavily on chance. Reality is clearly a mix of these two, where individuals only end up seeing some opportunities to form relationships. There is some chance in which relationships they have an opportunity to form, and then they use discretion in which ones of those they follow through on. This appears to be a potentially very useful future avenue of research.

Хачпанов Гия Вячеславович

В статье расписан путь развития со ссылкой на авторитетов, представлены и проанализированы графики.
Комментарии: 2

Turmanidze Tamila

In our opinion, one limitation faced by an incentive-based approach to modeling network formation is that many of the models that are analytically tractable end up with some limitations on their range. They can provide broad insights regarding things and they can help explain why one might see small worlds, and some other prominent characteristics of observed networks. However, many of the models are quite stark in their detail, and as a result end up with networks that are quite simple emerging as the stable and/or the client of networks. Networks like stars are quite special, and rarely observed in real social settings. While these can be thought of as analogs to hub-and-spoke sorts of networks, it is clear that the models are not so well suited in terms of trying to match the observed form of many large social networks, where there is a huge amount of heterogeneity in the network structures. There are two ways to deal with this. One is to work with simulations and agent-based modeling to introduce heterogeneity. Another is to bring in some randomness to the settings. Random network models have provided some simple models that end up providing insights into some observed networks. Such random models, however, end up being somewhat mechanical and new processes can be needed every time some difference in network structure is observed empirically. On the one hand the economic approach leans too heavily on choice and at the other extreme random network models lean too heavily on chance. Reality is clearly a mix of these two, where individuals only end up seeing some opportunities to form relationships. There is some chance in which relationships they have an opportunity to form, and then they use discretion in which ones of those they follow through on. This appears to be a potentially very useful future avenue of research.

Хачпанов Гия Вячеславович

В статье расписан путь развития со ссылкой на авторитетов, представлены и проанализированы графики.
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