TY - GEN

T1 - Improved bounds on the price of stability in network cost sharing games

AU - Lee, Euiwoong

AU - Ligett, Katrina

PY - 2013

Y1 - 2013

N2 - We study the price of stability in undirected network design games with fair cost sharing. Our work provides multiple new pieces of evidence that the true price of stability, at least for special subclasses of games, may be a constant. We make progress on this long-outstanding problem, giving a bound of O(log log log n) on the price of stability of undirected broadcast games (where n is the number of players). This is the first progress on the upper bound for this problem since the O(log log n) bound of [Fiat et al. 2006] (despite much attention, the known lower bound remains at 1.818, from [Bilo et al. 2010]). Our proofs introduce several new techniques that may be useful in future work. We provide further support for the conjectured constant price of stability in the form of a comprehensive analysis of an alternative solution concept that forces deviating players to bear the entire costs of building alternative paths. This solution concept includes all Nash equilibria and can be viewed as a relaxation thereof, but we show that it preserves many properties of Nash equilibria. We prove that the price of stability in multicast games for this relaxed solution concept is Θ(1), which may suggest that similar results should hold for Nash equilibria. This result also demonstrates that the existing techniques for lower bounds on the Nash price of stability in undirected network design games cannot be extended to be super-constant, as our relaxation concept encompasses all equilibria constructed in them.

AB - We study the price of stability in undirected network design games with fair cost sharing. Our work provides multiple new pieces of evidence that the true price of stability, at least for special subclasses of games, may be a constant. We make progress on this long-outstanding problem, giving a bound of O(log log log n) on the price of stability of undirected broadcast games (where n is the number of players). This is the first progress on the upper bound for this problem since the O(log log n) bound of [Fiat et al. 2006] (despite much attention, the known lower bound remains at 1.818, from [Bilo et al. 2010]). Our proofs introduce several new techniques that may be useful in future work. We provide further support for the conjectured constant price of stability in the form of a comprehensive analysis of an alternative solution concept that forces deviating players to bear the entire costs of building alternative paths. This solution concept includes all Nash equilibria and can be viewed as a relaxation thereof, but we show that it preserves many properties of Nash equilibria. We prove that the price of stability in multicast games for this relaxed solution concept is Θ(1), which may suggest that similar results should hold for Nash equilibria. This result also demonstrates that the existing techniques for lower bounds on the Nash price of stability in undirected network design games cannot be extended to be super-constant, as our relaxation concept encompasses all equilibria constructed in them.

KW - Network design

KW - Price of stability

UR - http://www.scopus.com/inward/record.url?scp=84879759779&partnerID=8YFLogxK

U2 - 10.1145/2492002.2482562

DO - 10.1145/2492002.2482562

M3 - Conference contribution

AN - SCOPUS:84879759779

SN - 9781450319621

T3 - Proceedings of the ACM Conference on Electronic Commerce

SP - 607

EP - 619

BT - EC 2013 - Proceedings of the 14th ACM Conference on Electronic Commerce

PB - Association for Computing Machinery

T2 - 14th ACM Conference on Electronic Commerce, EC 2013

Y2 - 16 June 2013 through 20 June 2013

ER -