# American Institute of Mathematical Sciences

October  2016, 3(4): 303-318. doi: 10.3934/jdg.2016016

## Network formation games with teams

 1 INRIA Sophia-Antipolis, 2004 route des Lucioles, 06902 Sophia-Antipolis, France, France, France

Received  October 2015 Revised  March 2016 Published  October 2016

Network formation games have been proposed as a tool to explain the topological characteristics of existing networks. They assume that each node is an autonomous decision-maker, ignoring that in many cases different nodes are under the control of the same authority (e.g. an Autonomous System) and then they operate as a team. In this paper we introduce the concept of network formation games for teams of nodes and show how very different network structures can arise also for some simple games studied in the literature. Beside extending the usual definition of pairwise stable networks to this new setting, we define a more general concept of stability toward deviations from a specific set $\mathcal{C}$ of teams' coalitions ($\mathcal{C}$-stability). We study then a trembling-hand dynamics, where at each time a coalition of teams can create or sever links in order to reduce its cost, but it can also take wrong decisions with some small probability. We show that this stochastic dynamics selects $\mathcal{C}$-stable networks or networks from closed cycles in the long run as the error probability vanishes.
Citation: Konstantin Avrachenkov, Giovanni Neglia, Vikas Vikram Singh. Network formation games with teams. Journal of Dynamics & Games, 2016, 3 (4) : 303-318. doi: 10.3934/jdg.2016016
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