Pure exchange economy: Set of multiple equilibria endowments

External question — Economics Stack Exchange Author: Giskard Original post: https://economics.stackexchange.com/questions/19290 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Initial endowments which can result in multiple equilibria in a pure exchange economy are explained here . Given a pure exchange economy, that is given the utility functions (which fulfil the usual properties) and total amounts of each good, what are some properties of the set of 'multiple equilibria endowment points'? Is this set connected? If yes, is it convex? Are there additional properties, does a charaterization (a set of necessary and sufficient properties) exist?

External answer — Economics Stack Exchange Author: Jovan Jezdic Original post: https://economics.stackexchange.com/a/57662 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. The following article: TODA, A.A. and WALSH, K.J., 2017. Edgeworth box economies with multiple equilibria. Economic Theory Bulletin, 5(1), pp. 65-80. though not focusing on the properties of the sets of endowment points that have multiple equilibria, provides a detailed look at the properties of utility functions that give way to the possibility of multiple equilibria. It examines CRRA, quadratic, quasi-linear, and general additively separable preferences in great detail and could provide some guidance for answering your question.