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ABSTRACT
Consider a model with finite number of goods, and with buyers with private values and quasi-linear utility functions. A domain of valuation functions for a buyer is a monotonicity domain if every finite-valued monotone randomized allocation rule defined on it is implementable, in the sense that there exists a randomized truth-telling direct mechanism that implements this allocation rule. We prove that a domain of valuations of dimension at least 2 is a monotonicity domain if and only if its closure is convex. INDEX TERMS
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