Journal of the ACM (JACM)
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the twenty-second annual symposium on Principles of distributed computing
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Selfish Routing in Capacitated Networks
Mathematics of Operations Research
The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On nash equilibria for a network creation game
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Stackelberg thresholds in network routing games or the value of altruism
Proceedings of the 8th ACM conference on Electronic commerce
Convergence time to Nash equilibrium in load balancing
ACM Transactions on Algorithms (TALG)
The price of anarchy in network creation games
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Game Theory
Online multicast with egalitarian cost sharing
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Convergence and approximation in potential games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
On Strong Equilibria in the Max Cut Game
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Approximating pure nash equilibrium in cut, party affiliation, and satisfiability games
Proceedings of the 11th ACM conference on Electronic commerce
Computing stable outcomes in hedonic games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Leading dynamics to good behavior
ACM SIGecom Exchanges
Computing stable outcomes in hedonic games with voting-based deviations
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Decentralized dynamics for finite opinion games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
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Many natural games have both high and low cost Nash equilibria: their Price of Anarchy is high and yet their Price of Stability is low. In such cases, one could hope to move behavior from a high cost equilibrium to a low cost one by a "public service advertising campaign" encouraging players to follow the low-cost equilibrium, and if every player follows the advice then we are done. However, the assumption that everyone follows instructions is unrealistic. A more natural assumption is that some players will follow them, while other players will not. In this paper we consider the question of to what extent can such an advertising campaign cause behavior to switch from a bad equilibrium to a good one even if only a fraction of people actually follow the given advice, and do so only temporarily. Unlike the "value of altruism" model, we assume everyone will ultimately act in their own interest. We analyze this question for several important and widely studied classes of games including network design with fair cost sharing, scheduling with unrelated machines, and party affiliation games (which include consensus and cut games). We show that for some of these games (such as fair cost sharing), a random α fraction of the population following the given advice is sufficient to get a guarantee within an O(1/α) factor of the price of stability for any α 0. For other games (such as party affiliation games), there is a strict threshold (in this case, α 1/2 is enough to reach near-optimal behavior). Finally, for some games, such as scheduling, no value α