Strategy-proof redistribution mechanisms for budget constrained bidders

We develop strategy-proof redistribution mechanisms when bidders have budget limitations. The budget limitation is one of realistic constraints for bidders. There have been several redistributionmechanisms under the assumption of quasi-linear utility functions. As a class of strategy-proof redistributionmechanisms, the partition mechanism has been proposed that divides the bidders into two partitions. Furthermore, in multi-unit auction mechanism for budget constrained bidders, a strategy-proof partition mechanism has been developed that can calculate an appropriate threshold price by using bidding information including gross utility and budget limitation. In this paper, by integrating these techniques, we study partitionmechanisms that guarantee strategy-proof and budget balance for budget constrained bidders. There exist the flows of information related to the bidders, redistribution payments, and unsold goods among partitions. We provide a condition on the flows so that a partitionmechanism can satisfy strategy-proofness as long as the mechanism applied in each partition is strategy-proof. Furthermore, we develop the three mechanisms as examples that satisfy this condition.