A Fixed Point Approach for the Computation of Market Equilibria

In proposing an open problem, Codenotti et al.[3, 5] conjectured that the welfare adjustment scheme can approximate the general market equilibrium by iteratively using an oracle for the Fisher’s model. In this work, we analyze the scheme for a large class of market models. We show that the iterative step is in fact a Lipschitz continuous function and the residue approximation of its fixed point is a good approximation of the market equilibrium price.

[1]  Xiaotie Deng,et al.  On the complexity of price equilibria , 2003, J. Comput. Syst. Sci..

[2]  Christos H. Papadimitriou,et al.  Exponential lower bounds for finding Brouwer fixed points , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[3]  Sriram V. Pemmaraju,et al.  On the polynomial time computation of equilibria for certain exchange economies , 2005, SODA '05.

[4]  T. Negishi.  WELFARE ECONOMICS AND EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1960 .

[5]  Rolf R Mantel.  The Welfare Adjustment Process: Its Stability Properties , 1971 .

[6]  Bruno Codenotti,et al.  Market equilibrium via the excess demand function , 2005, STOC '05.

[7]  Amin Saberi,et al.  Approximating Market Equilibria , 2003, RANDOM-APPROX.

[8]  Yinyu Ye.  Computing the Arrow-Debreu Competitive Market Equilibrium and Its Extensions , 2005, AAIM.

[9]  K. Arrow,et al.  EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1954 .

[10]  Kamal Jain,et al.  A Polynomial Time Algorithm for Computing the Arrow-Debreu Market Equilibrium for Linear Utilities , 2004, FOCS.

[11]  Kamal Jain,et al.  A polynomial time algorithm for computing an Arrow-Debreu market equilibrium for linear utilities , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[12]  Nikhil R. Devanur.  The spending constraint model for market equilibrium: algorithmic, existence and uniqueness results , 2004, STOC '04.

[13]  Sriram V. Pemmaraju,et al.  The computation of market equilibria , 2004, SIGA.

[14]  Sriram V. Pemmaraju,et al.  Algorithms Column: The Computation of Market Equilibria , 2004 .