Market Equilibrium via a Primal-Dual-Type Algorithm
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Auction algorithms for market equilibrium
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
An auction-based market equilibrium algorithm for a production model
WINE'05 Proceedings of the First international conference on Internet and Network Economics
An auction-based market equilibrium algorithm for a production model
Theoretical Computer Science
The Complexity of Models of International Trade
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
An auction-based market equilibrium algorithm for a production model
WINE'05 Proceedings of the First international conference on Internet and Network Economics
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We study the problem of computing equilibrium prices in a Fisher market with linear utilities and linear single-constraint production units. This setting naturally appears in ad pricing where the sum of the lengths of the displayed ads is constrained not to exceed the available ad space. There are three approaches to solve market equilibrium problems: convex programming, auction-based algorithms, and primal-dual. Jain, Vazirani, and Ye recently proposed a solution using convex programming for the problem with an arbitrary number of production constraints. A recent paper by Kapoor, Mehta, and Vazirani proposes an auction-based solution. No primal-dual algorithm is proposed for this problem. In this paper we propose a simple reduction from this problem to the classical Fisher setting with linear utilities and without any production units. Our reduction not only imports the primal-dual algorithm of Devanur et al. to the single-constraint production setting, but also: i) imports other simple algorithms, like the auction-based algorithm of Garg and Kapoor, thereby providing a simple insight behind the recent sophisticated algorithm of Kapoor, Mehta, and Vazirani, and ii) imports all the nice properties of the Fisher setting, for example, the existence of an equilibrium in rational numbers, and the uniqueness of the utilities of the agents at the equilibrium.