Quality of local equilibria in discrete exchange economies |
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Affiliation: | 1. Aix-Marseille University, CNRS, EHESS, Centrale Marseille, AMSE, Marseille, France;2. EDHEC Business School, France |
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Abstract: | This paper defines the notion of a local equilibrium of quality , , in a discrete exchange economy: a partial allocation and item prices that guarantee certain stability properties parametrized by the numbers and . The quality measures the fit between the allocation and the prices: the larger and the closer the fit. For this notion provides a graceful degradation for the conditional equilibria of Fu, Kleinberg and Lavi (2012) which are exactly the local equilibria of quality . For the local equilibria of quality are more stable than conditional equilibria. Any local equilibrium of quality provides, without any assumption on the type of the agents’ valuations, an allocation whose value is at least the optimal fractional allocation. In any economy in which all agents’ valuations are -submodular, i.e., exhibit complementarity bounded by , there is a local equilibrium of quality . In such an economy any greedy allocation provides a local equilibrium of quality . Walrasian equilibria are not amenable to such graceful degradation. |
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Keywords: | Discrete exchange economies Local equilibria Item prices |
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