The density and complexity of polynomial cores for intractable sets
Information and Control
The complexity of optimization problems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences
Generalizations of Opt P to the polynomial hierarchy
Theoretical Computer Science
On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Market equilibria for homothetic, quasi-concave utilities and economies of scale in production
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Leontief economies encode nonzero sum two-player games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The computational complexity of nash equilibria in concisely represented games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Junta distributions and the average-case complexity of manipulating elections
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
An auction-based market equilibrium algorithm for a production model
Theoretical Computer Science
Algorithmic Game Theory
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
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The convexity assumptions required for the Arrow-Debreu theorem are reasonable and realistic for preferences; however, they are highly problematic for production because they rule out economies of scale. We take a complexity-theoretic look at economies with non-convex production. It is known that in such markets equilibrium prices may not exist; we show that it is an intractable problem to achieve Pareto efficiency, the fundamental objective achieved by equilibrium prices. The same is true for core efficiency or any one of an array of concepts of stability, with the degree of intractability ranging from F Δ2P-completeness to PSPACE-hardness. We also identify a novel phenomenon that we call complexity equilibrium in which agents quiesce, not because there is no way for any one of group of them to improve their situation, but because discovering the changes necessary for (individual or group) improvement is intractable. In fact, we exhibit a somewhat natural distribution of economies that has an average-case hard complexity equilibrium.