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Infrastructure Resilience Conference 2018

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From Individuals Decisions to Emerging Social Structure

“Man is by nature a social animal” was claimed by Arisostle and since then sociologists and economists studied how human beings continuously adapt their behaviour to the surrounding society, while acting selfishly. Individuals pay attention to their reputation and typically they can decide who they want to be friend with and how much to invest in their relationships. We believe that macroscopic features of real-world social networks as those described by the sociologists can be viewed as the effect of a strategic network formation process where individuals can revise their weighted outgoing links (representing the commitment in their friendships) while trying to maximize their values of centrality (reputation), provided that ties have a cost.

In this paper we consider the centrality game in which a set of homogeneous individuals play random sequential best response dynamics. The benefit in the payoff function is given by a locally assessable Katz centrality measure and a clustering factor, reflecting the fact that, in the language of social networks, the friend of your friend is likely also to be your friend. Each individual also incurs a cost, proportional to his/her commitment in his/her friendships, but overall the payoff function exhibits positive externalities, namely the welfare of a single individual is increased by others’ linking actions.

We characterize “stable” networks through the notion of Nash equilibrium and we use the variational inequality approach in order to derive the necessary (and sufficient) conditions on the agent’s preferences so that a democratic Nash equilibrium emerges in the form of a complete network. We also establish sufficient conditions for attractivity of the complete network, which is shown to be a social optimum in these cases. We believe that introducing heterogeneity among individuals will break the symmetry of the problem, thus leading to more interesting equilibria in terms of real-world social networks features.

Nicolò Pagan
ETH Zürich


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