Core-selecting auctions with incomplete information

Abstract

Core-selecting auctions were proposed recently as alternatives to the VCG mechanism for environments with complementarities. While the Vickrey auction yields efficiency in pure private values models, this efficiency may come at the cost of extremely low seller revenues and a high vulnerability to collusion and shill bidding. By contrast, core-selecting auctions may result in "competitive" outcomes which seem to mitigate the problems of the Vickrey auction. Ausubel and Milgrom (2002), Ausubel, Cramton and Milgrom (2006), Day and Raghavan (2007), Day and Milgrom (2008) and Day and Cramton (2008) have advocated selling complementary goods using core-selecting auctions or two-stage procedures incorporating a core-selecting auction. Moreover, this research has been taken seriously by policymakers; for example, the UK has already implemented two spectrum auctions using the package clock auction, in which the second stage is a core-selecting auction (Cramton, 2009). However, while the VCG mechanism is best motivated by its dominant-strategy property under incomplete information, the existing literature on core-selecting auctions performs only a completeinformation analysis. In this paper, we consider a simple incomplete-information model with two goods, two "local" bidders, and one "global bidder". We examine a parametric family of distributions in which, at one extreme, the local bidders' valuations are independent and, at the other extreme, the local bidders' valuations are perfectly correlated. We perform a full equilibrium analysis for four different coreselecting auction formats, including the nearest-Vickrey rule advocated by Day and Raghavan (2007) and Day and Cramton (2008), as well as the proxy auction of Ausubel and Milgrom (2002).

Full Implementation and Belief Restrictions

“…Agents are assigned to group 1 independently with probability p , and they inherit the type of their group, drawn independently from a distribution with mean E (θ) . An agent's type is his private information, his group is known to the designer but not to the other agents (e.g., Ausubel and Baranov 2013). In this model it is common knowledge…”

Computing Bayes-Nash Equilibria in Combinatorial Auctions with Continuous Value and Action Spaces

“…This domain has been widely studied, and analytical BNE results for it are available under several mechanisms. Ausubel and Baranov (2013) study the case where the global bidder's valuation is drawn from U[0, 2], while the local bidders' valuations are drawn from U[0, 1], with distribution F (v) = v α . Furthermore, the local bidders' valuations are perfectly correlated with probability γ, and independent otherwise.…”

“…Adopting their results as our benchmark, we assemble a set of 16 auction settings to be used as a test suite: four payment rules each applied to four domains (α ∈ {1, 2} × γ ∈ {0, 0.5}). Note that our selection of settings covers all payment rules for which analytical results are known and all interesting regions in the (α, γ)-parameter space for which the analytical results have distinct functional forms (Ausubel & Baranov, 2013). 7 Importantly, we did not exclude any settings for modeling or algorithmic tractability reasons.…”

“…Thus, in LLG, computing the ε-BNE only involves computing the strategies for the local bidders. Furthermore, to match the analytical results of Ausubel and Baranov (2013), we only consider symmetric equilibria in this domain (though this simplification is not essential to our algorithm). Thus, the whole strategy profile in LLG can be described by one function s local : [0, 1] → R ≥0 .…”

On the clock of the combinatorial clock auction

“… We do not consider the “core‐selecting” elements in the pricing rule of real‐world CCAs (see, e.g., Day and Milgrom 2008, Day and Cramton 2012, and Erdil and Klemperer 2010, as well as Goeree and Lien 2016 and Ausubel and Baranov 2019). …”