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

Abstract

We analyze first-price equilibrium bidding behavior of capacityconstrained firms in a sequence of two procurement auctions. In the model, firms with a cost advantage in completing the project auctioned off at the end of the sequence may enter the unfavored first auction hoping to lose it. Equilibrium bidding in both auctions deviates from the standard Symmetric Independent Private Value auction model due to opportunity costs of bidding created by possibly employed capacity. For this sequential auction model with non-identical objects, we show that revenue equivalence applies.Keywords Sequential first-price auctions · Revenue equivalence · Endogenous outside options · Procurement auction · Capacity constraintsWe thank Werner Güth and Ulf Schiller for helpful comments and stimulating discussions. The paper greatly benefited from very helpful comments of the associate editor and two reviewers. We gratefully acknowledge comments from

Optimal capacity provision for service providers with subsequent auctioning of projects

“…She shows the critical influence ordering can have on the efficiency of an auction. For a similar set-up, Reiß and Schöndube (2010) studied revenue equivalence in a sequential auction with capacity constrained bidders. While these models consider bidders who only participate once in an auction, we consider bidders who participate repeatedly.…”

A sequential procurement model for a PPP project pipeline

“…The theoretical model of Jofre-Bonet and Pesendorfer [19] and the empirical studies by De Silva et al [10] and Wolfram [49] account for endogenously appearing asymmetries due to synergies, but in the PPP setting bidders may ex ante differ in the cost probability distributions which is also the case in the work of Reiβ and Schöndube [37]. Moreover, in contrast to models that study infinite timeframes (e.g., [16,33,38,52]), the PPP pipeline has a finite nature which is a logical consequence of the magnitude of the projects and the limited budget horizon of governments.…”

“…Alternatively, the objects can be homogeneous in nature in the sense that they are perfect substitutes [22,53]. Finally, the objects may have the same stochastic feature and are said to be stochastically equivalent [12,[37][38].…”

“…Whereas Katzman [22] and Katehakis and Puranam [21] for instance do not include a capacity constraint, the contributions of Engelbrecht-Wiggans [12], Milgrom and Weber [29], Elmaghraby [11] and Reiβ and Schöndube [37] assume a singleunit demand. Other studies include monetary constraints [36] or restrict the availability of manhours [43].…”

A Sequential Procurement Model for a PPP Project Pipeline

“…Apart from the type of the tendered objects, modeling approaches also differ in their consideration of the capacity constraints. Whereas Katzman [22] and Katehakis and Puranam [21] for instance do not include a capacity constraint, the contributions of Engelbrecht-Wiggans [12], Milgrom and Weber [29], Elmaghraby [11] and Reiβ and Schöndube [37] assume a singleunit demand. Other studies include monetary constraints [36] or restrict the availability of manhours [43].…”