Atabati, Omid and Farzad, Babak (2014): A strategic model for network formation. Published in: Computational Social Networks , Vol. 2, No. 1 (1 February 2015): pp. 114.

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Abstract
We study the dynamics of a gametheoretic network formation model that yields largescale smallworld networks. So far, mostly stochastic frameworks have been utilized to explain the emergence of these networks. On the other hand, it is natural to seek for gametheoretic network formation models in which links are formed due to strategic behaviors of individuals, rather than based on probabilities. Inspired by EvenDar and Kearns' model [8], we consider a more realistic framework in which the cost of establishing each link is dynamically determined during the course of the game. Moreover, players are allowed to put transfer payments on the formation and maintenance of links. Also, they must pay a maintenance cost to sustain their direct links during the game. We show that there is a small diameter of at most 4 in the general set of equilibrium networks in our model. We achieved an economic mechanism and its dynamic process for individuals which firstly; unlike the earlier model, the outcomes of players' interactions or the equilibrium networks are guaranteed to exist. Furthermore, these networks coincide with the outcome of pairwise Nash equilibrium in network formation. Secondly; it generates largescale networks that have a rational and strategic microfoundation and demonstrate the main characterization of small degree of separation in reallife social networks. Furthermore, we provide a network formation simulation that generates smallworld networks.
Item Type:  MPRA Paper 

Original Title:  A strategic model for network formation 
Language:  English 
Keywords:  network formation; linking game with transfer payments; pairwise stability; pairwise Nash equilibrium; smallworld phenomenon 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C79  Other D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D85  Network Formation and Analysis: Theory 
Item ID:  62529 
Depositing User:  Omid Atabati 
Date Deposited:  03 Mar 2015 11:32 
Last Modified:  29 Mar 2017 11:24 
References:  1. M. Bayati, C. Borgs, J. Chayes, Y. Kanoria, and A. Montanari. Bargaining dynamics in exchange networks. In ACMSIAM Symp on Discrete Algorithms, pages 1518{1537, 2011. 2. F. Bloch and M. O. Jackson. De�nitions of equilibrium in network formation games. Int J Game Theory, 34(3):305{318, 2006. 3. F. Bloch and M. O. Jackson. The formation of networks with transfers among players. J Econom Theory, 133(1):83{110, 2007. 4. A. Calv�oArmengol and R. Ilkili�c. Pairwisestability and nash equilibria in network formation. Int J Game Theory, 38(1):51{79, 2009. 5. S. Chakrabarti and R. Gilles. Network potentials. Rev Econom Des, 11(1):13{52, 2007. 6. E. Y. Daraghmi and S. Yuan. We are so close, less than 4 degrees separating you and me! Computers in Human Behavior, 30:273{285, 2014. 7. J. de Mart�� and Y. Zenou. Social networks. IFN Working Paper No 816, 2009. 8. E. EvenDar and M. Kearns. A small world threshold for economic network formation. In Advances in Neural Information Processing Systems 19, pages 385{392, 2007. 9. A. Fabrikant, A. Luthra, E. N. Maneva, C. H. Papadimitriou, and S. Shenker. On a network creation game. In 22nd Annual ACM Symposium on Principles of Distributed Computing, pages 347{351, 2003. 10. E. Gallo. Essays in the economics of networks. PhD thesis, University of Oxford, Department of Economics, 2011. 11. T. Hellman. On the existence and uniqueness of pairwise stable networks. Int J Game Theory, 42:211{237, 2012. 12. M. O. Jackson. Social and Economic Networks. Princeton University Press, Princeton, NJ, 2008. 13. M. O. Jackson and A. Watts. The existence of pairwise stable networks. Seoul Journal of Economics, 14(3):299{321, 2001. 14. M. O. Jackson and A. Watts. The evolution of social and economic networks. Journal of Economic Theory, 106:265{295, 2002. 15. M. O. Jackson and A. Wolinsky. A strategic model of social and economic networks. Journal of Economic Theory, 71:44{74, 1996. 16. J. Kleinberg. The smallworld phenomenon: An algorithmic perspective. In Symposium on the Theory of Computing, pages 163{170, 2000. 17. S. Milgram. The small world problem. Psychology Today, 1:61{67, 1967. 18. R. Myerson. Game Theory: Analysis of Con ict. Harvard University Press, Cambridge, MA, 1991. 19. A. Watts. A dynamic model of network formation. Games and Economic Behavior, 34:331{341, 2001. 20. D. Watts and S. Strogatz. Collective dynamics of smallworld networks. Nature, 393:440{442, 1998. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/62529 