Non-cooperative facility location and covering games
Theoretical Computer Science
Improved lower bounds on the price of stability of undirected network design games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
On approximate nash equilibria in network design
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Designing Network Protocols for Good Equilibria
SIAM Journal on Computing
Optimal cost sharing protocols for scheduling games
Proceedings of the 12th ACM conference on Electronic commerce
Congestion games with variable demands
Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge
Restoring pure equilibria to weighted congestion games
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
On the Existence of Pure Nash Equilibria in Weighted Congestion Games
Mathematics of Operations Research
The ring design game with fair cost allocation
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Optimal Cost Sharing for Resource Selection Games
Mathematics of Operations Research
NP-hardness of pure Nash equilibrium in Scheduling and Network Design Games
Theoretical Computer Science
Slice embedding solutions for distributed service architectures
ACM Computing Surveys (CSUR)
Price of stability in polynomial congestion games
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
On Nash Equilibria for a Network Creation Game
ACM Transactions on Economics and Computation
Hi-index | 0.00 |
We consider a model of game-theoretic network design initially studied by Anshelevich et al. (Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS), pp. 295–304, 2004), where selfish players select paths in a network to minimize their cost, which is prescribed by Shapley cost shares. If all players are identical, the cost share incurred by a player for an edge in its path is the fixed cost of the edge divided by the number of players using it. In this special case, Anshelevich et al. (Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS), pp. 295–304, 2004) proved that pure-strategy Nash equilibria always exist and that the price of stability—the ratio between the cost of the best Nash equilibrium and that of an optimal solution—is Θ(log k), where k is the number of players. Little was known about the existence of equilibria or the price of stability in the general weighted version of the game. Here, each player i has a weight w i ≥1, and its cost share of an edge in its path equals w i times the edge cost, divided by the total weight of the players using the edge. This paper presents the first general results on weighted Shapley network design games. First, we give a simple example with no pure-strategy Nash equilibrium. This motivates considering the price of stability with respect to α-approximate Nash equilibria—outcomes from which no player can decrease its cost by more than an α multiplicative factor. Our first positive result is that O(log w max )-approximate Nash equilibria exist in all weighted Shapley network design games, where w max is the maximum player weight. More generally, we establish the following trade-off between the two objectives of good stability and low cost: for every α=Ω(log w max ), the price of stability with respect to O(α)-approximate Nash equilibria is O((log W)/α), where W is the sum of the players’ weights. In particular, there is always an O(log W)-approximate Nash equilibrium with cost within a constant factor of optimal. Finally, we show that this trade-off curve is nearly optimal: we construct a family of networks without o(log w max / log log w max )-approximate Nash equilibria, and show that for all α=Ω(log w max /log log w max ), achieving a price of stability of O(log W/α) requires relaxing equilibrium constraints by an Ω(α) factor.