Collaboration in Social Networks

30 Pages Posted: 19 Jan 2012

See all articles by Luca Dall'Asta

Luca Dall'Asta

Collegio Carlo Alberto

Matteo Marsili

Abdus Salam International Centre for Theoretical Physics (ICTP)

Paolo Pin

Dipartimento di Economia Politica, Università degli Studi di Siena

Date Written: January 17, 2012

Abstract

The very notion of social network implies that linked individuals interact repeatedly with each other. This allows them not only to learn successful strategies and adapt to them, but also to condition their own behavior on the behavior of others, in a strategic forward looking manner. Game theory of repeated games shows that these circumstances are conducive to the emergence of collaboration in simple games of two players. We investigate the extension of this concept to the case where players are engaged in a local contribution game and show that rationality and credibility of threats identify a class of Nash equilibria – that we call “collaborative equilibria” – that have a precise interpretation in terms of sub-graphs of the social network. For large network games, the number of such equilibria is exponentially large in the number of players. When incentives to defect are small, equilibria are supported by local structures whereas when incentives exceed a threshold they acquire a non-local nature, which requires a “critical mass” of more than a given fraction of the players to collaborate. Therefore, when incentives are high, an individual deviation typically causes the collapse of collaboration across the whole system. At the same time, higher incentives to defect typically support equilibria with a higher density of collaborators. The resulting picture conforms with several results in sociology and in the experimental literature on game theory, such as the prevalence of collaboration in denser groups and in the structural hubs of sparse networks.

Keywords: repeated games, social networks, phase transitions

JEL Classification: C72, C73, D85

Suggested Citation

Dall'Asta, Luca and Marsili, Matteo and Pin, Paolo, Collaboration in Social Networks (January 17, 2012). Available at SSRN: https://ssrn.com/abstract=1986812 or http://dx.doi.org/10.2139/ssrn.1986812

Luca Dall'Asta (Contact Author)

Collegio Carlo Alberto ( email )

via Real Collegio 30
Moncalieri, Torino 10024
Italy

Matteo Marsili

Abdus Salam International Centre for Theoretical Physics (ICTP) ( email )

Strada Costiera 11
Trieste, 34014
Italy

Paolo Pin

Dipartimento di Economia Politica, Università degli Studi di Siena ( email )

Piazza San Francesco 8
Siena, I53100
Italy

HOME PAGE: http://www.econ-pol.unisi.it/paolopin/

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
92
Abstract Views
918
rank
357,382
PlumX Metrics