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(Near) Substitute Preferences and Equilibria with Indivisibilities

Algorithms, Approximation, and Learning in Market and Mechanism Design November 06, 2023 - November 09, 2023

November 07, 2023 (11:45 AM PST - 12:30 PM PST)
Speaker(s): Rakesh Vohra (University of Pennsylvania)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Tags/Keywords
  • Competitive Equilibrium

  • Indivisible

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(Near) Substitute Preferences and Equilibria with Indivisibilities

Abstract

An obstacle to using market mechanisms to allocate indivisible goods (such as courses to students) is the non-existence of competitive equilibria (CE). To surmount this, Arrow and Hahn proposed the notion of social-approximate equilibria: a price vector and corresponding excess demands that are `small'. We identify a class of preferences called $\Delta$-substitutes, and show that social approximate equilibria where the bound on excess demand, good-by-good, is $2(\Delta-1)$ independent of the size of the economy. When $\Delta=1$ existence of CE is guaranteed even in the presence of income effects. This sufficient condition strictly generalizes prior conditions.

These results rely on a new type of Shapley-Folkman-Starr Lemma which could be of independent interest.

This is joint work with Thanh Nguyen.

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(Near) Substitute Preferences and Equilibria with Indivisibilities

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