Heuristic Algorithms for Scheduling Independent Tasks on Nonidentical Processors
Journal of the ACM (JACM)
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
The price of anarchy is independent of the network topology
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On nash equilibria for a network creation game
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
(Almost) optimal coordination mechanisms for unrelated machine scheduling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient coordination mechanisms for unrelated machine scheduling
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Conflicting Congestion Effects in Resource Allocation Games
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Coordination mechanisms for selfish scheduling
Theoretical Computer Science
Convergence time to Nash equilibria
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
| Hi-index | 0.00 |
The price of anarchy [16] is by now a standard measure for quantifying the inefficiency introduced in games due to selfish behavior, and is defined as the ratio between the optimal outcome and the worst Nash equilibrium. However, this notion is well defined only for games that always possess a Nash equilibrium (NE). We propose the dynamic inefficiency measure, which is roughly defined as the average inefficiency in an infinite best-response dynamic. Both the price of anarchy [16] and the price of sinking [9] can be obtained as special cases of the dynamic inefficiency measure. We consider three natural best-response dynamic rules -- Random Walk (RW), Round Robin (RR) and Best Improvement (BI) -- which are distinguished according to the order in which players apply best-response moves. In order to make the above concrete, we use the proposed measure to study the job scheduling setting introduced in [3], and in particular the scheduling policy introduced there. While the proposed policy achieves the best possible price of anarchy with respect to a pure NE, the game induced by the proposed policy may admit no pure NE, thus the dynamic inefficiency measure reflects the worst case inefficiency better. We show that the dynamic inefficiency may be arbitrarily higher than the price of anarchy, in any of the three dynamic rules. As the dynamic inefficiency of the RW dynamic coincides with the price of sinking, this result resolves an open question raised in [3]. We further use the proposed measure to study the inefficiency of the Hotelling game and the facility location game. We find that using different dynamic rules may yield diverse inefficiency outcomes; moreover, it seems that no single dynamic rule is superior to another.