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Can Markets Compute Equilibria?, Hunter Monroe

Abstract
Recent turmoil in financial and commodities markets has renewed questions regarding how well markets discover equilibrium prices, particularly when those markets are highly complex. A relatively new critique questions whether markets can realistically find equilibrium prices if computers cannot. For instance, in a simple exchange economy with Leontief preferences, the time required to compute equilibrium prices using the fastest known techniques is an exponential function of the number of goods. Furthermore, no efficient technique for this problem exists if a famous mathematical conjecture is correct. The conjecture states loosely that there are some problems for which finding an answer (i.e., an equilibrium price vector) is hard even though it is easy to check an answer (i.e., that a given price vector is an equilibrium). This paper provides a brief overview of computational complexity accessible to economists, and points out that the existence of computational problems with no best solution algorithm is relevant to this conjecture
Table Of Contents
Contents; I. Introduction; II. Is Computing Equilibria Difficult?; Table; 1. Payoff Matrix for the Prisoner's Dilemma; Figures; 1. NP-complete: Is there a Hamilton Cycle?; 2. P: Is this a Hamilton Cycle?; III. Are There Natural Problems with No Best Algorithm?; A. Superlinear vs. Blum Speedup; B. No Best Algorithm for Integer and Matrix Multiplication?; 3. Boolean circuit: Are at least two inputs "TRUE"?; C. The Power of Cancellation; D. No Best Algorithm for coNP-Complete Problems?; E. No Best Algorithm Versus No Algorithm at All; IV. Conclusion; 4. Is speedup inherited?; References
Language
eng
Literary Form
non fiction
Edition
1st ed.
Note
Description based upon print version of record
Physical Description
1 online resource (22 p.)
Specific Material Designation
remote
Form Of Item
online
Isbn
9781452797502

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