Sequential partition mechanism for strongly budget-balanced redistribution

We propose a new class of strategy-proof and strongly budget-balanced redistribution mechanisms called the sequential partition mechanism (SPM). Recently, studies on redistribution mechanisms have attracted increased attention in the research area of mechanism design to achieve a desirable social decision among self-interested agents. However, since no redistribution mechanism can simultaneously satisfy Pareto efficiency, strategy-proofness, individual rationality, and is strongly budget-balanced, we need to sacrifice one of these properties. In the SPM, agents and items are divided into groups, and then a strategy-proof mechanism is sequentially applied to each group. The payments in each group are distributed among agents in the remaining groups in a predefined way. The auctioneer can dynamically determine how to divide agents and items and which mechanism to apply, based on the results of previous auctions. As an instance of the SPM, we introduce the redistribution mechanism based on a take-it-or-leave-it auction (RM-TLA) mechanism. The RM-TLA does not require agents to reveal a bidding price. Thus, the agents only have to accept/reject the offered price. Furthermore, we show that we can set the optimal reserve price so that the expected social surplus is maximized if an auctioneer knows the distribution of an agent's valuation in advance.