A Primal-Dual Algorithm for Computing Fisher Equilibrium in the Absence of Gross Substitutability Property

Abstract. We provide the first strongly polynomial time exact combinatorial algorithm to compute Fisher equilibrium for the case when utility functions do not satisfy the Gross substitutability property. The motivation for this comes from the work of Kelly, Maulloo, and Tan [15] and Kelly and Vazirani [16] on rate control in communication networks. We consider a tree like network in which root is the source and all the leaf nodes are the sinks. Each sink has got a fixed amount of money which it can use to buy the capacities of the edges in the network. The edges of the network sell their capacities at certain prices. The objective of each edge is to fix a price which can fetch the maximum money for it and the objective of each sink is to buy capacities on edges in such a way that it can facilitate the sink to pull maximum flow from the source. In this problem, the edges and the sinks play precisely the role of sellers and buyers, respectively, in the Fisher’s market model. The ut...

• Type: Conference
• Year: 2005
• Where: WINE
• Authors: Dinesh Garg, Kamal Jain, Kunal Talwar, Vijay V. Vazirani
• Keywords: Economy, Equilibrium Prices, Exact Combinatorial Algorithm, Gross Substitutability Property, WINE 2005