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.
%0 Journal Article
%1 DallAsta2011Collaboration
%A Dall'Asta, Luca
%A Marsili, Matteo
%A Pin, Paolo
%D 2011
%K social-networks cascades
%T Collaboration in Social Networks
%U http://arxiv.org/abs/1104.2026
%X 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.
@article{DallAsta2011Collaboration,
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.}},
added-at = {2019-06-10T14:53:09.000+0200},
archiveprefix = {arXiv},
author = {Dall'Asta, Luca and Marsili, Matteo and Pin, Paolo},
biburl = {https://www.bibsonomy.org/bibtex/2fd9aa8ca3e9996031fe6be36069c55be/nonancourt},
citeulike-article-id = {9146080},
citeulike-linkout-0 = {http://arxiv.org/abs/1104.2026},
citeulike-linkout-1 = {http://arxiv.org/pdf/1104.2026},
day = 11,
eprint = {1104.2026},
interhash = {c4b52d2aeb42e8801040010b66c4b9a6},
intrahash = {fd9aa8ca3e9996031fe6be36069c55be},
keywords = {social-networks cascades},
month = apr,
posted-at = {2011-04-12 11:49:56},
priority = {2},
timestamp = {2019-07-31T12:52:15.000+0200},
title = {{Collaboration in Social Networks}},
url = {http://arxiv.org/abs/1104.2026},
year = 2011
}