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Exact and Approximate Equilibria for Optimal Group Network Elliot Anshelevich

Summary: Exact and Approximate Equilibria for Optimal Group Network
Elliot Anshelevich
Bugra Caskurlu
December 2009
We consider a process called Group Network Formation Game, which represents the scenario when
strategic agents are building a network together. In our game, agents can have extremely varied connec-
tivity requirements, and attempt to satisfy those requirements by purchasing links in the network. We
show a variety of results about equilibrium properties in such games, including the fact that the price
of stability is 1 when all nodes in the network are owned by players, and that doubling the number of
players creates an equilibrium as good as the optimum centralized solution. For the general case, we show
the existence of a 2-approximate Nash equilibrium that is as good as the centralized optimum solution,
as well as how to compute good approximate equilibria in polynomial time. Our results essentially imply
that for a variety of connectivity requirements, giving agents more freedom can paradoxically result in
more efficient outcomes.
1 Introduction
Many modern computer networks, including the Internet itself, are constructed and maintained by self-
interested agents. This makes network design a fundamental problem for which it is important to understand
the effects of strategic behavior. Modeling and understanding of the evolution of nonphysical networks


Source: Anshelevich, Elliot - Department of Computer Science, Rensselaer Polytechnic Institute


Collections: Computer Technologies and Information Sciences