Fair Groves mechanisms

We study allocation problems in which a costly task is to be assigned and money transfers are used to achieve fairness among agents. We consider a series of fairness notions (k-fairness for where n is the number of agents) of decreasing restrictiveness that are based on Rawls’ maximin equity criterion and impose welfare lower bounds. These fairness notions were introduced by Porter et al. (J Econ Theory 118:209–228, 2004) who also introduced two classes of Groves mechanisms that are 1-fair and 3-fair, respectively, and generate deficits that are bounded above. We show that these classes are the largest such classes of Groves mechanisms. We generalize these mechanisms for each and show that the corresponding mechanisms generate the smallest deficit for each economy among all k-fair Groves mechanisms. The first draft of this paper was written while we were Ph.D. students at the University of Rochester. We are grateful to William Thomson for his guidance and advice. We also thank two referees and the associate editor for their comments.