Constructing pure-exchange economies with many equilibria

Pascal Gauthier (), Timothy Kehoe and Erwan Quintin ()
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Pascal Gauthier: Nordic Investment Bank
Erwan Quintin: University of Wisconsin–Madison

Economic Theory, 2022, vol. 73, issue 2, No 9, 564 pages

Abstract: Abstract We develop a restart algorithm based on Scarf’s (The Computation of Economic Equilibria, Yale University Press, 1973) algorithm for computing approximate Brouwer fixed points. We use the algorithm to compute all of the equilibria of a general equilibrium pure-exchange model with four consumers, four goods, and 15 equilibria. The mathematical result that motivates the algorithm is a fixed-point index theorem that provides a sufficient condition for uniqueness of equilibrium and a necessary condition for multiplicity of equilibria. Examining the structure of the model with 15 equilibria provides us with a method for constructing higher dimensional models with even more equilibria. For example, using our method, we can construct a pure-exchange economy with eight consumers and eight goods that has (at least) 255 equilibria.

Keywords: Uniqueness of equilibrium; Multiplicity of equilibrium; Computation of equilibrium (search for similar items in EconPapers)
JEL-codes: C60 C62 C63 D51 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00199-021-01406-0

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