Asymmetric reduced form Auctions

Abstract

This paper provides a tractable characterization of feasibility of asymmetric reduced form auctions. Using this, auction design problems can be stated in terms of the reduced form only. This allows to solve optimal auction problems when classical solution techniques fail. AbstractThis paper provides a tractable characterization of feasibility of asymmetric reduced form auctions. Using this, auction design problems can be stated in terms of the reduced form only. This allows to solve optimal auction problems when classical solution techniques fail.

Efficient mechanisms with information acquisition

“…Recall that h is the probability measure on W corresponding to H(z). Then D is σ(L 2 , L 2 ) compact by a proof similar to that of Lemma 5.4 in Border (1991) and Lemma 8 in Mierendorff (2011). Therefore, after taking subsequences again, Q νκ converges to Q in σ(L 2 , L 2 ) topology and Q ∈ D. Because z ∈ L 2 and h ∈ L 2 , the weak convergence of {Q νκ } implies that w w zQ(z)h(z)dz = V (α * ).…”

“…] denote the support of w i for all i. By Theorem 3 in Mierendorff (2011), Q is implementable if and only if it satisfies…”

Optimal dynamic mechanism design with deadlines

“…the condition that the object be allocated only once, is formulated in terms of interim winning probabilities. We use the characterization of feasibility of asymmetric reduced form allocation rules in Mierendorff (2008) to solve the resulting control problem.…”

“…Said (2008) also considers the efficient allocation rule for the model described above and shows that the mechanism derived in Bergemann and Välimäki (2008) can be implemented by a sequence of open auctions. Mierendorff (2009) shows that the efficient allocation of a single object with stochastically arriving long-lived bidders with privately known time preferences only requires transfers between the seller and the winning bidder. Pavan, Segal, and Toikka (2008) consider a very general dynamic mechanism design model with a fixed set of agents who receive one-dimensional private information in every period.…”

“…For an early application of a special case of the result see Maskin and Riley (1984). Che, Condorelli and Kim (private communication) independently derived the characterization of feasibility in Mierendorff (2008). 5 Recently, Hellwig (2008) has derived a version of Pontriyagin's maximum principle that allows for a monotonicity constraint on the control variable without requiring absolute continuity.…”