A multi-item auction with budget-constrained bidders and price controls

•We consider a multi-item auction model with unit-demand bidders.•Both budget constraints and price controls are allowed.•A rationed equilibrium whose allocation is in the core is proposed.•An ascending auction is constructed to find the proposed equilibrium.

We extend the multi-item auction model of Talman and Yang (2008) and Andersson et al. (2015) by considering both unit-demand bidders with budget constraints and price controls on bidding items. Due to these budget and price restrictions, a Walrasian equilibrium generally fails to exist. To achieve efficiency, we propose a rationed equilibrium whose allocation is in the core. We also construct an ascending auction to find the proposed rationed equilibrium in (pseudo-)polynomial time.