Crowding games are sequentially solvable
International Journal of Game Theory
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
On approximating optimal auctions
Proceedings of the 3rd ACM conference on Electronic Commerce
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
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
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Nashification and the coordination ratio for a selfish routing game
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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We study fundamental algorithmic questions concerning the complexity of market equilibria under perfect and imperfect information by means of a basic microeconomic game. Suppose a provider offers a service to a set of potential customers. Each customer has a particular demand of service and her behavior is determined by a utility function that is nonincreasing in the sum of demands that are served by the provider.Classical game theory assumes complete information: the provider has full knowledge of the behavior of all customers. We present a complete characterization of the complexity of computing optimal pricing strategies and of computing best/worst equilibria in this model. Basically, we show that most of these problems are inapproximable in the worst case but admit an FPAS in the average case. Our average case analysis covers large classes of distributions for customer utilities. We generalize our analysis to robust equilibria in which players change their strategies only when this promises a significant utility improvement.A more realistic model considers providers with incomplete information. Following the game theoretic framework of Bayesian games introduced by Harsanyi, the provider is aware of probability distributions describing the behavior of the customers and aims at estimating its expected revenue under best/worst equilibria. Somewhat counterintuitively, 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 problems increases with the precision of the available knowledge.