Abstract
This paper defines the notion of a local equilibrium of quality (r,s), 0≤r,s, in a discrete exchange economy: a partial allocation and item prices that guarantee certain stability properties parametrized by the numbers r and s. The quality (r,s) measures the fit between the allocation and the prices: the larger r and s the closer the fit. For r,s≤1 this notion provides a graceful degradation for the conditional equilibria of Fu, Kleinberg and Lavi (2012) which are exactly the local equilibria of quality (1,1). For 1<r,s the local equilibria of quality (r,s) are more stable than conditional equilibria. Any local equilibrium of quality (r,s) provides, without any assumption on the type of the agents’ valuations, an allocation whose value is at least [Formula presented] the optimal fractional allocation. In any economy in which all agents’ valuations are a-submodular, i.e., exhibit complementarity bounded by a≥1, there is a local equilibrium of quality [Formula presented]. In such an economy any greedy allocation provides a local equilibrium of quality (1,1a). Walrasian equilibria are not amenable to such graceful degradation.
Original language | English |
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Pages (from-to) | 141-152 |
Number of pages | 12 |
Journal | Journal of Mathematical Economics |
Volume | 88 |
DOIs | |
State | Published - May 2020 |
Bibliographical note
Publisher Copyright:© 2020 Elsevier B.V.
Keywords
- Discrete exchange economies
- Item prices
- Local equilibria