Allocating bandwidth for bursty connections
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Crowding games are sequentially solvable
International Journal of Game Theory
On approximating optimal auctions
Proceedings of the 3rd ACM conference on Electronic Commerce
On the complexity of equilibria
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Hardness of Optimal Auctions
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Market Equilibrium via a Primal-Dual-Type Algorithm
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
Random knapsack in expected polynomial time
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Stochastic Load Balancing and Related Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On finding the exact solution of a zero-one knapsack problem
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Probabilistic analysis of knapsack core algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Nashification and the coordination ratio for a selfish routing game
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Fairness and optimality in congestion games
Proceedings of the 6th ACM conference on Electronic commerce
Selfish routing with incomplete information
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Average-Case and Smoothed Competitive Analysis of the Multilevel Feedback Algorithm
Mathematics of Operations Research
Graphical congestion games with linear latencies
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Evolutionary equilibrium in Bayesian routing games: Specialization and niche formation
Theoretical Computer Science
On the existence of pure strategy nash equilibria in integer-splittable weighted congestion games
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
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We study algorithmic questions concerning a basic microeconomic congestion game in which there is a single provider that offers a service to a set of potential customers. Each customer has a particular demand of service and the behavior of the customers is determined by utility functions that are non-increasing in the congestion. Customers decide whether to join or leave the service based on the experienced congestion and the offered prices. Following standard game theory, we assume each customer behaves in the most rational way. If the prices of service are fixed, then such a customer behavior leads to a pure, not necessarily unique Nash equilibrium among the customers. In order to evaluate marketing strategies, the service provider is interested in estimating its revenue under the best and worst customer equilibria. We study the complexity of this problem under different models of information available to the provider.•We first consider the classical model in which the provider has perfect knowledge of the behavior of all customers. We present a complete characterization of the complexity of computing optimal pricing strategies and of computing best and worst equilibria. Basically, we show that most of these problems are inapproximable in the worst case but admit an "average-case FPAS." Our average case analysis covers general distributions for customer demands and utility thresholds. We generalize our analysis to robust equilibria in which players change their strategies only when this promises a significant utility improvement.•We extend our analysis to a more realistic model in which the provider has incomplete information. Following the game theoretic framework of Bayesian games introduced by Harsanyi, we assume that the provider is aware of probability distributions describing the behavior of the customers and aims at estimating its expected revenue under best and worst equilibria. Somewhat counterintuitive, we obtain an FPRAS for the equilibria problem in the model with imperfect information although the problem with perfect information is inapproximable under the worst case measures. In particular, the worst case complexity of the considered stochastic equilibria problems increases with the precision of the available knowledge.