Implementation in multidimensional dichotomous domains. Issue 2 (16th May 2013)

• Record Type: Journal Article
• Authors: Mishra, Debasis; Roy, Souvik
• Is Part Of: Theoretical economics. Volume 8:Issue 2(2013:May)
• Page Start: 431
• Page End: 466
• Publication Date: 2013-05-16
• Subjects: Economics -- Periodicals; 330.01
• DOI: 10.3982/TE1239
• Languages: English
• ISSNs: 1933-6837

Abstract

<abstract abstract-type="main" xml:lang="en"> <title> <x xml:space="preserve">Abstract</x> </title> <p>We consider deterministic dominant strategy implementation in multidimensional <italic>dichotomous</italic> 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.</p> </abstract>