Abstract
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.
Highlights
Network formation games are nowadays a consolidated branch of game theory
To the best of our knowledge this is the first paper where the concept of teams is introduced in network formation games
We extend the concept of pairwise stable networks to this new class of games, and define a new concept of network stability toward deviations from a specific set C of teams’ coalitions
Summary
Network formation games are nowadays a consolidated branch of game theory (see for example the recent books [6], [5], [10], [9]). In network formation games with teams we consider that nodes belonging to each set Ti share the same cost c(Ti, g) As a consequence, they will form or sever links only if this is beneficial for the whole set Ti, i.e. if the cost of Ti is reduced. We introduce teams in a network creation game considered by Corbo and Parkes [4] and we observe that some different stable network structure arises even for very simple cases Jackson and Watts [12] considered dynamic formation of networks in standard network formation games without teams, where at each time only a pair of players are selected and only a link between them can be changed
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