1 research outputs found
Network Connection Games with Disconnected Equilibria
In this paper we extend a popular non-cooperative network creation game (NCG)
to allow for disconnected equilibrium networks. There are n players, each is a
vertex in a graph, and a strategy is a subset of players to build edges to. For
each edge a player must pay a cost \alpha, and the individual cost for a player
represents a trade-off between edge costs and shortest path lengths to all
other players. We extend the model to a penalized game (PCG), for which we
reduce the penalty counted towards the individual cost for a pair of
disconnected players to a finite value \beta. Our analysis concentrates on
existence, structure, and cost of disconnected Nash and strong equilibria.
Although the PCG is not a potential game, pure Nash equilibria always and pure
strong equilibria very often exist. We provide tight conditions under which
disconnected Nash (strong) equilibria can evolve. Components of these
equilibria must be Nash (strong) equilibria of a smaller NCG. However, in
contrast to the NCG, for almost all parameter values no tree is a stable
component. Finally, we present a detailed characterization of the price of
anarchy that reveals cases in which the price of anarchy is \Theta(n) and thus
several orders of magnitude larger than in the NCG. Perhaps surprisingly, the
strong price of anarchy increases to at most 4. This indicates that global
communication and coordination can be extremely valuable to overcome socially
inferior topologies in distributed selfish network design.Comment: 18 pages, 4 figures, extended abstract in WINE 200