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We show that the problem of finding an ǫ-approximate Nash equilibrium of an n × n two-person games can be reduced to the computation of an (ǫ/n) 2-approximate market equilibrium of a Leontief economy. Together with a recent result of Chen, Deng and Teng, this polynomial reduction implies that the Leontief market exchange problem does not have a fully… (More)

We study a Walrasian equilibrium model to determine the prices of CPU time. The customers have jobs that require a given length of CPU slot allocation with their valuations dependent on the assigned time slots. The owner of the CPU processing time receives compensation for time slots sold to the customers, subject to the condition that the slots sold to a… (More)

We introduce a new family of utility functions for exchange markets. This family provides a natural and " continuous " hybridization of the traditional linear and Leontief utilities and might be useful in understanding the complexity of computing and approximating of market equilibria. We show that a Fisher equilibrium of an exchange market with m… (More)

We consider the computational complexity of the market equilibrium problem by exploring the structural properties of the Leontief exchange economy. We prove that, for economies guaranteed to have a market equilibrium, finding one with maximum social welfare or maximum individual welfare is NP-hard. In addition, we prove that counting the number of… (More)

We consider a social optimization model of pricing scheme in single-minded auctions , in cases where Walrasian equilibrium does not exist. We are interested in maximization of the ratio, R, of happy bidders over all agents, in a feasible allocation-pricing scheme. We show NP-hardness of the optimization problem, establish lower and upper bounds of R, as… (More)