Abstract
We consider deterministic dominant strategy implementation in multidimensional dichotomous domains in a private values and quasilinear utility setting. In such multidimensional domains, an agent’s type is characterized by a single number, the value of the agent, and a nonempty set of acceptable alternatives. Each acceptable alternative gives the agent utility equal to his value and other alternatives give him zero utility. We identify a new condition, which we call generation monotonicity, that is necessary and sufficient for implementability in any dichotomous domain. If such a domain satisfies a richness condition, then a weaker version of generation monotonicity, which we call 2-generation monotonicity (equivalent to 3-cycle monotonicity), is necessary and sufficient for implementation. We use this result to derive the optimal mechanism in a one-sided matching problem with agents who have dichotomous types.
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