Strong equilibrium in cost sharing connection games

Abstract

We study network games in which each player wishes to connect his source and sink, and the cost of each edge is shared among its users either equally (in Fair Connection Games-FCG's) or arbitrarily (in General Connection Games-GCG's). We study the existence and quality of strong equilibria (SE)-strategy profiles from which no coalition can improve the cost of each of its members-in these settings. We show that SE always exist in the following games: (1) Single source and sink FCG's and GCG's.(2) Single source multiple sinks FCG's and GCG's on series parallel graphs. (3) Multi source and sink FCG's on extension parallel graphs. As for the quality of the SE, in any FCG with n players, the cost of any SE is bounded by H (n) (i.e., the harmonic sum), contrasted with the Θ(n) price of anarchy. For any GCG, any SE is optimal.

The Complexity of Equilibria in Cost Sharing Games

“…-For the case of Singleton Cost Sharing Games our algorithm does not output just a PNE but a Strong Nash Equilibrium. Hence this extends the results in [6] on the existence of Strong Nash Equilibria in Cost Sharing Games. -Our second main result is that computing a PNE in the class of Network Cost Sharing Games where the cost functions come from the Shapley Cost Sharing Mechanism, f (x) = c r /x (Fair Cost Allocation) is PLS-complete.…”

“…However, they do not always exist in Cost Sharing Games. When they exist Epstein et al [6] show that their worst case quality matches the PoS bound of H n . Balcan et al [3] study Cost Sharing Games with Fair Cost Allocation under the perspective of Learning Agents.…”

“…Later Charikar et al [4] improve this bound to O(log 3 n)OP T and also make progress for the case when best response and sequential arriving is interleaved. Epstein et al [6] study the quality of Strong Nash Equilibria of Cost Sharing Games with Fair Cost Allocation. Strong Nash Equilibria allow for group moves of players, therefore they are a solution concept robust to collusion.…”

Improved Bounds for Facility Location Games with Fair Cost Allocation

“…The facility location game is a special case of the general network design game model with fair cost allocation proposed in [1], which has attracted a significant amount of recent research [5][6][7][8].…”

“…Albers recently considered general network design with weighted players [5]; she proved an almost tight poly-logarithmic lower bound on the P oS for PNE and studied the Price of Anarchy of approximate SE with weighted and unweighted agents. SE of network design games were first studied by Epstein et al [6]. The notion of SE is due to Aumann [11].…”