Angelo Fanelli

Improved Lower Bounds on the Price of Stability of Undirected Network Design Games

Bounding the price of stability of undirected network design games with fair cost allocation is a challenging open problem in the Algorithmic Game Theory research agenda. Even though the generalization of such games in directed networks is well understood in terms of the price of stability (it is exactly Hn, the n-th harmonic number, for games with n players), far less is known for network design games in undirected networks. The upper bound carries over to this case as well while the best known lower bound is 42/23≈1.826. For more restricted but interesting variants of such games such as broadcast and multicast games, sublogarithmic upper bounds are known while the best known lower bound is 12/7≈1.714. In the current paper, we improve the lower bounds as follows. We break the psychological barrier of 2 by showing that the price of stability of undirected network design games is at least 348/155≈2.245. Our proof uses a recursive construction of a network design game with a simple gadget as the main building block. For broadcast and multicast games, we present new lower bounds of 20/11≈1.818 and 1.862, respectively.

Efficient Computation of Approximate Pure Nash Equilibria in Congestion Games

Congestion games constitute an important class of games in which computing an exact or even approximate pure Nash equilibrium is in general {\sf PLS}-complete. We present a surprisingly simple polynomial-time algorithm that computes

Graphical Congestion Games

O(1)

When ignorance helps: Graphical multicast cost sharing games

-approximate Nash equilibria in these games. In particular, for congestion games with linear latency functions, our algorithm computes

The Speed of Convergence in Congestion Games under Best-Response Dynamics

(2+\epsilon)

Improved lower bounds on the price of stability of undirected network design games

-approximate pure Nash equilibria in time polynomial in the number of players, the number of resources and

Nash Stability in Fractional Hedonic Games

1/\epsilon

Dynamics of profit-sharing games

. It also applies to games with polynomial latency functions with constant maximum degree

The ring design game with fair cost allocation

d

Game Theoretical Issues in Optical Networks

; there, the approximation guarantee is