Collaboration in Social Networks
Luca Dall'Asta, Matteo Marsili, Paolo Pin

TL;DR
This paper explores how collaboration emerges and sustains in social networks through game-theoretic analysis of local contribution games, revealing the impact of incentives, network structure, and rationality on equilibrium states.
Contribution
It introduces the concept of 'collaborative equilibria' in network games, linking them to sub-graphs and analyzing their properties in large networks.
Findings
Number of equilibria grows exponentially with network size.
High incentives lead to non-local, system-wide collaboration.
Denser networks and hubs promote collaboration.
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,…
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