Standard Auctions with Financially Constrained Bidders

Abstract

We develop a methodology for analyzing the revenue and efficiency performance of auctions when buyers have private information about their willingness to pay and ability to pay. We then apply the framework to scenarios involving standard auction mechanisms. In the simplest case, where bidders face absolute spending limits, first-price auctions yield higher expected revenue and social surplus than second-price auctions. The revenue dominance of first-price auctions over secondprice auctions carries over to the case where bidders have access to credit. These rankings are explained by differences in the extent to which financial constraints bind in different auction formats.

Auctions Where Incomes are Private Information and Preferences (Non Quasi-Linear) are Common Knowledge

“…Che and Gale (1998) show that it is possible to have a symmetric equilibrium in a first price auction where bids are equal to incomes and the expected revenue in first price auctions will be strictly higher than the expected revenue in second price auctions. In our model, when incomes are low enough, valuations are exactly equal to incomes (see (1)).…”

“…We show that bidder's valuation can never exceed his income. We also show that depending on the nature of the utility 1 As per convention, we use capital letters to denote random variables and corresponding small letters to denote the realised values of such variables. 2 See Krishna (2010) for all the standard results around the benchmark model.…”

“…He (she) only knows that ∀j 6 = i, V j lies in the interval [v, v] with a known distribution function 1 . Seller also does not know any bidder's valuation.…”

First-price equilibrium and revenue equivalence in a sequential procurement auction model

“…From a geometric point of view, there arise isobid curves in two-dimensional type space. This approach was introduced in Che and Gale (1998). Che and Gale (1998) incorporate financial constraints into the SIPV model where the first dimension of the type is the value of the auctioned object and the second dimension is the financial constraint, e.g., the budget available for purchasing the object.…”

“…Che and Gale (1998) incorporate financial constraints into the SIPV model where the first dimension of the type is the value of the auctioned object and the second dimension is the financial constraint, e.g., the budget available for purchasing the object. Interestingly, equilibrium aggregation of two-dimensional types in Che and Gale (1998) leads to a (refined) minimum selection of type dimensions, the result that revenue equivalence does not hold and "Leontief" isobid curves for the first-price and second-price auction. In our paper, the second dimension is the cost of executing a project that is offered in a second auction which is related to the option value of winning the second auction.…”