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JDG

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.

keywords:
teams
,
Network formation games
,
strong stability
,
$\mathcal{C}$-stability
,
stochastic stability.

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