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2017 / Grabisch, M., A. Mandel, A. Rusinowska and E. Tanimura

Strategic influence in social networks

Mathematics of Operations Research, Vol. 43, 29-50
We consider a model of influence with a set of nonstrategic agents and two strategic agents. The nonstrategic agents have initial opinions and are linked through a simply connected network. They update their opinions as in the DeGroot model. The two strategic agents have fixed and opposed opinions. They each form a link with a nonstrategic agent in order to influence the average opinion that emerges due to interactions in the network. This procedure defines a zero-sum game whose players are the two strategic agents and whose strategy set is the set of nonstrategic agents. We focus on the existence and the characterization of pure strategy equilibria in this setting. Simple examples show that the existence of a pure strategy equilibrium does depend on the structure of the network. We characterize equilibrium with two notions: the influenceability of target agents, and their centrality, which in our context we call “intermediacy.” We also show that when the two strategic agents have the same impact, symmetric equilibria emerge as natural solutions. In the case where the impacts are uneven, the game has only equilibria in mixed strategies, the high impact agent focuses on his own centrality/intermediacy and the influenceability of his opponent’s target while the low influence agent focuses on the influenceability of his own target.
2016 / LiCalzi, M. and N. Maagli

Bargaining over a common categorisation

Synthese, Vol. 193, 705-723
Two agents endowed with different categorisations engage in bargaining to reach an understanding and agree on a common categorisation. We model the process as a simple non-cooperative game and demonstrate three results. When the initial disagreement is focused, the bargaining process has a zero-sum structure. When the disagreement is widespread, the zero-sum structure disappears and the unique equilibrium requires a retraction of consensus: two agents who individually associate a region with the same category end up rebranding it under a different category. Finally, we show that this last equilibrium outcome is Pareto dominated by a cooperative solution that avoids retraction; that is, the unique equilibrium agreement may be inefficient.
2014 / Colombo, L., G. Femminis and A. Pavan

Information Acquisition and Welfare

The Review of Economic Studies, Vol. 81, 1438–1483
We study information acquisition in a flexible framework with strategic complementarity or substitutability in actions and a rich set of externalities that are responsible for possible wedges between the equilibrium and the efficient acquisition of information. First, we relate the (in)efficiency in the acquisition of information to the (in)efficiency in the use of information and explain why efficiency in the use does not guarantee efficiency in the acquisition. Next, we show how the acquisition of private information affects the social value of public information (i.e., the comparative statics of equilibrium welfare with respect to the quality of public information). Finally, we illustrate the implications of our results in a few applications that include beauty contests, monetary economies with price-setting complementarities, and economies with negative production externalities
2013 / Quax R., A. Apolloni and P.M.A. Sloot 

The diminishing role of hubs in dynamical processes on complex networks

Journal of the Royal Society Interface,, Vol. 10(88)
It is notoriously difficult to predict the behaviour of a complex self-organizing system, where the interactions among dynamical units form a heterogeneous topology. Even if the dynamics of each microscopic unit is known, a real understanding of their contributions to the macroscopic system behaviour is still lacking. Here, we develop information-theoretical methods to distinguish the contribution of each individual unit to the collective out-of-equilibrium dynamics. We show that for a system of units connected by a network of interaction potentials with an arbitrary degree distribution, highly connected units have less impact on the system dynamics when compared with intermediately connected units. In an equilibrium setting, the hubs are often found to dictate the long-term behaviour. However, we find both analytically and experimentally that the instantaneous states of these units have a short-lasting effect on the state trajectory of the entire system. We present qualitative evidence of this phenomenon from empirical findings about a social network of product recommendations, a protein–protein interaction network and a neural network, suggesting that it might indeed be a widespread property in nature.
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