Theoretical Economics 8 (2013), 431–466

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### Implementation in multidimensional dichotomous domains

*Debasis Mishra, Souvik Roy*

#### Abstract

We consider deterministic dominant strategy implementation in multidimensional dichotomous domains in private values and quasi-linear utility setting. In such multidimensional domains, an agentâ€™s type is characterized by a single number, the value of the agent, and a non-empty set of acceptable alternatives. Each acceptable alternative gives the agent utility equal to his value and other alternatives give him zero utility. We identity 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 having dichotomous types.

Keywords: Dominant strategy implementation, cycle monotonicity, dichotomous preferences, generation monotonicity

JEL classification: C78, C79, D02, D44

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