Trading mechanism selection with budget constraints

We present an equilibrium search model of competing mechanisms where some buyers are budget constrained. Absent budget constraints, the existing literature capitulates that if buyers differ in their valuations then in the unique equilibrium all sellers hold second price auctions (e.g. McAfee (1993)) whereas if buyers are homogeneous then sellers are indifferent across a large number of payoff-equivalent mechanisms (e.g. Eeckhout and Kircher (2010)). We show that these results are not robust to the presence of budget constrained buyers; merely lowering the budgets of a few buyers renders the auction equilibrium as well as payoff equivalence unsustainable. If buyers differ only slightly in terms of their ability to pay then sellers prefer fixed price trading; otherwise they prefer auctions.