{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T07:27:28Z","timestamp":1767770848228},"reference-count":36,"publisher":"Proceedings of the National Academy of Sciences","issue":"12","content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2012,3,20]]},"abstract":"<jats:p>The very notion of social network implies that linked individuals interact repeatedly with each other. This notion 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\u2014that we call \u201ccollaborative equilibria\u201d\u2014that have a precise interpretation in terms of subgraphs 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 nonlocal nature, which requires a \u201ccritical mass\u201d 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.<\/jats:p>","DOI":"10.1073\/pnas.1105757109","type":"journal-article","created":{"date-parts":[[2012,3,3]],"date-time":"2012-03-03T17:46:14Z","timestamp":1330796774000},"page":"4395-4400","update-policy":"http:\/\/dx.doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":25,"title":["Collaboration in social networks"],"prefix":"10.1073","volume":"109","author":[{"given":"Luca","family":"Dall\u2019Asta","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy;"},{"name":"The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy;"},{"name":"Collegio Carlo Alberto, Via Real Collegio 30, 10024 Moncalieri (Torino), Italy; and"}]},{"given":"Matteo","family":"Marsili","sequence":"additional","affiliation":[{"name":"The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy;"}]},{"given":"Paolo","family":"Pin","sequence":"additional","affiliation":[{"name":"Dipartimento di Economia Politica, Universit\u00e1 degli Studi di Siena, Piazza San Francesco 7, 53100 Siena, Italy"}]}],"member":"341","published-online":{"date-parts":[[2012,3]]},"reference":[{"key":"e_1_3_3_1_2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400833993"},{"key":"e_1_3_3_2_2","first-page":"597","volume-title":"Am J Soc","author":"Homans CG","year":"1958","unstructured":"CG Homans, Social Behavior as Exchange. 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