Local Equilibria

07/01/2018

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by   Daniel Lehmann, et al.

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A local equilibrium is a generalization of a Walrasian, i.e., competitive equilibrium. Many exchange economies that have no Walrasian equilibrium have local equilibria. Local equilibria always provide, without any assumption on the type of the agents, an allocation whose value is at least half that of the, even fractional, optimal allocation. Existence of a local equilibrium is not guaranteed. If the valuation of every agent is submodular, the existence of a local equilibrium is guaranteed and any greedy allocation provides a local equilibrium.