Implementation in multidimensional dichotomous domains - Debasis Mishra; Souvik Roy (Theoretical Economics, 2013)
We consider deterministic dominant strategy implementation in multidimensional dichotomous domains in private values and quasi-linear utility setting. In such multidimensional domains, an agent'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: C78; C79; D02; D44; 330; Dominant strategy implementation; cycle monotonicity; dichotomous preferences; generation monotonicity