Choosing `Me' and `My Friends': Identity in a Non-Cooperative Network Formation Game with Cost Sharing

Dev, Pritha (2010): Choosing `Me' and `My Friends': Identity in a Non-Cooperative Network Formation Game with Cost Sharing.

Abstract

This paper introduces the choice of identity characteristics, and, commitments to these characteristics, in a network formation model where links costs are shared. Players want to link to the largest group given that linking costs are decreasing (increasing) in commitments for same (different) identity. We study conditions under which these choices allow for networks with multiple identities. We find that whether the choice of identity itself gives any utility or not, there will be Nash networks featuring multiple identities. Moreover, if the choice of identity directly adds utility, networks with multiple identities will be efficient and survive the dynamic process.

• Item Type: MPRA Paper
• Language: English
• Keywords: Identity, Network Formation, Cost Sharing Links
• Subjects: Z - Other Special Topics > Z1 - Cultural Economics ; Economic Sociology ; Economic Anthropology > Z13 - Economic Sociology ; Economic Anthropology ; Social and Economic Stratification; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D85 - Network Formation and Analysis: Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Akerlof, G. A., and R. E. Kranton (2000): \Economics And Identity," The Quarterly Journal of Economics, 115(3), 715{753.

Bala, V., and S. Goyal (2000a): \A Noncooperative Model of Network Formation," Econometrica, 68(5), 1181{1230.

Bala, V., and S. Goyal (2000b): \A strategic analysis of network reliability," Review of Economic Design, 5(3), 205{228.

Bisin, A., and T. Verdier (2000): \\Beyond The Melting Pot" : Cultural Transmission, Marriage, And The Evolution Of Ethnic And Religious Traits," The Quarterly Journal of Economics, 115(3), 955{988.

Bloch, F., and M. O. Jackson (2007): \The formation of networks with transfers among players," Journal of Economic Theory, 133(1), 83{110.

Bramoulle, Y., and R. Kranton (2007): \Public goods in networks," Journal of Economic Theory, 127(1), 478{494.

Chandra, K. (2001): \Ethnic Bargains, Group Instability and Social Choice Theory," Politics and Society, 29(3), 337{362.

Currarini, S., M. O. Jackson, and P. Pin (2008): \An Economic Model of Friendship: Homophily, Minorities and Segregation," Econometrica, 77(4), 1003{1045.

Currarini, S., and M. Morelli (2000): \Network Formation with Sequential Demands," Royal Holloway, University of London: Discussion Papers in Economics 99/2, Department of Economics, Royal Holloway University of London.

Deroan, F. (2003): \Farsighted strategies in the formation of a communication network," Economics Letters, 80(3), 343{349.

Dev, P. (2009): \Identity and Fragmentation in Networks," Mimeo, ITAM.

Dutta, B., and M. O. Jackson (2003): Networks and Groups: Models of Strategic Formation. Springer- Verlag.

Esteban, J., and D. Ray (1994): \On the Measurement of Polarization," Econometrica, 62(4), 819{51.

Feri, F. (2004): \Stochastic stability in networks with decay," Mimeo. University of Venice.

Fryer, R. G., and M. O. Jackson (2002): \Categorical Cognition: A Psychological Model of Categories and Identication in Decision Making," Microeconomics 0211002, EconWPA.

Galeotti, A. (2006): \One-way ow networks: the role of heterogeneity," Economic Theory, 29(1), 163{ 179.

Galeotti, A., S. Goyal, and J. Kamphorst (2006): \Network formation with heterogeneous players," Games and Economic Behavior, 54(2), 353{372.

Gilles, R., and S. Sarangi (2004): \Social network formation with consent," Discussion paper.

Gilles, R. P., and C. Johnson (2000): \Spatial social networks," Review of Economic Design, 5(3), 273{299.

Goyal, S., and S. Joshi (2003): \Networks of collaboration in oligopoly," Games and Economic Behavior, 43(1), 57{85.

Goyal, S., and F. Vega-Redondo (2005): \Network formation and social coordination," Games and Economic Behavior, 50(2), 178{207.

Hojman, D. A., and A. Szeidl (2008): \Core and periphery in networks," Journal of Economic Theory, 139(1), 295{309.

Horowitz, D. (1977): \Cultural Movements and Ethnic Change," Annals of the American Academy of Political and Social Science, 433(1), 6{18.

Jackson, M. O. (2005): \The Economics of Social Networks," Proceedings of the 9th World Congress of the Econometric Society, edited by Richard Blundell, Whitney Newey, and Torsten Persson, Cambridge University Press, forthcoming.

Jackson, M. O., and B. Dutta (2000): \The stability and eciency of directed communication networks," Review of Economic Design, 5(3), 251{272.

Jackson, M. O., and A. Wolinsky (1996): \A Strategic Model of Social and Economic Networks," Journal of Economic Theory, 71(1), 44{74.

Kranton, R. E., and D. F. Minehart (2001): \A Theory of Buyer-Seller Networks," American Economic Review, 91(3), 485{508.

McBride, M. (2006): \Imperfect monitoring in communication networks," Journal of Economic Theory, 126(1), 97{119.

Mutuswami, S., and E. Winter (2002): \Subscription Mechanisms for Network Formation," Journal of Economic Theory, 106(2), 242{264.

Page Jr., F. H., and M. Wooders (2007): \Networks and clubs," Journal of Economic Behavior & Organization, 64(3-4), 406{425.

Page Jr., F. H., and M. Wooders (2009): \Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, 66(1), 462 { 487.

Sarangi, S., P. Billand, and C. Bravard (2006): \Heterogeneity in Nash Networks," Departmental Working Papers, Department of Economics,Louisiana State University.

Sen, A. (2006): Identity and Violence: The Illusion of Destiny. W. W. Norton.

Slikker, M., and A. van den Nouweland (2001): \A One-Stage Model of Link Formation and Payo Division," Games and Economic Behavior, 34(1), 153{175.

Watts, A. (2001): \A Dynamic Model of Network Formation," Games and Economic Behavior, 34(2), 331{341.