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# Strategic influence in social networks. Mathematics of Operations Research, 2017

## De M. Grabisch, A. Mandel, A. Rusinowska, E. Tanimura

Strategic influence in social networks.*Mathematics of Operations Research*, INFORMS, 2017, 30 p.

**Résumé/Abstract :**

We consider a model of influence with a set of non-strategic agents and two strategic agents.

The non-strategic 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 non-strategic 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 non-strategic 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. The characterization of equilibrium we obtain emphasizes on the one hand the influenceability of target agents and on the other hand their centrality whose characterization in our context induces a new notion that we call intermediacy.

We also show that in the case where the two strategic agents have the same impact, symmetric equilibria emerge as natural solutions whereas 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.

**Mots-clés JEL :**

C - Mathematical and Quantitative Methods/C.C7 - Game Theory and Bargaining Theory/C.C7.C72 - Noncooperative Games

**Citer la référence :**

Michel Grabisch, Antoine Mandel, Agnieszka Rusinowska, Emily Tanimura. Strategic influence in social networks. Mathematics of Operations Research, INFORMS, 2017, 30p. 〈10.1287/moor.2017.0853> <halshs-01493047〉

**DOI : **

**Notice HAL : **

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