A note on the impossibility of multi-unit auctions with budget-constrained bidders (Q6587050)

In this article, the author study auctions in the domain of decreasing marginal valuations and show that in the presence of budget-constrained bidders there is no multi-unit auction that satisfies the following four properties: incentive compatibility, Pareto optimality, individual rationality and no positive transfers. More precisely, the author prove an impossibility theorem for auctions with multiple bidders and multi-unit items that does not require the explicit and implicit assumptions on bidders' budgets made by \textit{H. F. Ting} and \textit{X. Xiang} [Lect. Notes Comput. Sci. 7676, 669--678 (2012; Zbl 1260.91115)]. This result strengthens the impossibility results of previous studies. Section 3 gives the basic impossibility result. Section 4 concludes with a brief discussion of the main theorem.