Weakly fair allocations and strategy-proofness

This paper investigates the problem of allocating two types of indivisible objects among a group of agents when a priority-order must be respected and only restricted monetary transfers are allowed. Since the existence of a fair (as in envy-free) allocation is not generally guaranteed, due to the restrictions on the money transfers, the concept of fairness is weakened, and a new concept of fairness is introduced. This concept is called weak fairness. This paper defines an allocation rule that implements weakly fair allocations and demonstrates that it is coalitionally strategy-proof. In fact, under a mild regulatory condition and quasi-linear utility functions, it is demonstrated that this is the only coalitionally strategy-proof allocation rule that implements a weakly fair allocation. We would like to thank two anonymous referees, the participants at the Society for the Advancement of Economic Theory Conference (Greece, 2007) and the participants at the Association for Public Economic Theory Meeting (Nashville, USA, 2007) for valuable comments. The authors would also like to acknowledge financial support from The Jan Wallander and Tom Hedelius Foundation.