Sharing the “cost” of multicast trees: an axiomatic analysis
IEEE/ACM Transactions on Networking (TON)
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third 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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Self-Interested Routing in Queueing Networks
Management Science
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 Routing Unsplittable Flow
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Fast convergence of selfish rerouting
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On nash equilibria for a network creation game
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Strong equilibrium in cost sharing connection games
Proceedings of the 8th ACM conference on Electronic commerce
The “Price of Anarchy” Under Nonlinear and Asymmetric Costs
Mathematics of Operations Research
Fast, Fair, and Efficient Flows in Networks
Operations Research
The Impact of Oligopolistic Competition in Networks
Operations Research
Approximate strong equilibrium in job scheduling games
Journal of Artificial Intelligence Research
Stackelberg Routing in Arbitrary Networks
Mathematics of Operations Research
Computer Science Review
Strong price of anarchy for machine load balancing
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Convergence of best-response dynamics in games with conflicting congestion effects
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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We study strategic resource allocation settings, where jobs correspond to self-interested players who choose resources with the objective of minimizing their individual cost. Our framework departs from the existing game-theoretic models mainly in assuming conflicting congestion effects, but also in assuming an unlimited supply of resources. In our model, a job's cost is composed of both its resource's load (which increases with congestion) and its share in the resource's activation cost (which decreases with congestion). We provide results for a job-scheduling setting with heterogeneous jobs and identical machines. We show that if the resource's activation cost is shared equally among its users, a pure Nash equilibrium (NE) might not exist. In contrast, the proportional sharing rule induces a game that admits a pure NE, which can also be computed in polynomial time. As part of the algorithm's analysis, we establish a new, nontrivial property of schedules obtained by the longest processing time algorithm. We also observe that, unlike in congestion games, best-response dynamics (BRD) are not guaranteed to converge to a Nash equilibrium. Finally, we measure the inefficiency of equilibria with respect to the minimax objective function, and prove that there is no universal bound for the worst-case inefficiency (as quantified by the “price of anarchy” measure). However, the best-case inefficiency (quantified by the “price of stability” measure) is bounded by 5/4, and this is tight. These results add another layer to the growing literature on the price of anarchy and stability, which studies the extent to which selfish behavior affects system efficiency.