Collusion-Resilient Revenue In Combinatorial Auctions

In auctions of a single good, the second-price mechanism achieves, in dominantstrategies, a revenue benchmark that is naturally high and resilient to anypossible collusion.We show how to achieve, to the maximum extent possible, the same propertiesin combinatorial auctions

Very Simple and Efficient Byzantine Agreement

We present a very simple, cryptographic, binary Byzantine-agreement protocol that, with n >= 3t+1 >= 3 players, at most t of which are malicious, halts in expected 9 rounds

Perfect Implementation

Privacy and trust aect our strategic thinking, yet they have not been precisely modeled in mechanism design. In settings of incomplete information, traditional implementations of a normal-form mechanism - by disregarding the players' privacy, or assuming trust in a mediator - may fail to reach the mechanism's objectives. We thus investigate implementations of a new type. We put forward the notion of a perfect implementation of a normal-form mechanism M: in essence, a concrete extensive-form mechanism exactly preserving all strategic properties of M, without relying on a trusted mediator or violating the privacy of the players. We prove that any normal-form mechanism can be perfectly implemented by a verifiable mediator using envelopes and an envelope-randomizing device (i.e., the same tools used for running fair lotteries or tallying secret votes). Differently from a trusted mediator, a veriable one only performs prescribed public actions, so that everyone can verify that he is acting properly, and that he never learns any information that should remain private

Knightian Analysis of the Vickrey Mechanism

We analyze the Vickrey mechanism for auctions of multiple identical goods when the players have both Knightian uncertainty over their own valuations and incomplete preferences. In this model, the Vickrey mechanism is no longer dominant-strategy, and we prove that all dominant-strategy mechanisms are inadequate. However, we also prove that, in undominated strategies, the social welfare produced by the Vickrey mechanism in the worst case is not only very good, but also essentially optimal.Comment: To appear in Econometric

Knightian Auctions

We study single-good auctions in a setting where each player knows his own valuation only within a constant multiplicative factor \delta{} in (0,1), and the mechanism designer knows \delta. The classical notions of implementation in dominant strategies and implementation in undominated strategies are naturally extended to this setting, but their power is vastly different. On the negative side, we prove that no dominant-strategy mechanism can guarantee social welfare that is significantly better than that achievable by assigning the good to a random player. On the positive side, we provide tight upper and lower bounds for the fraction of the maximum social welfare achievable in undominated strategies, whether deterministically or probabilistically

Rational Robustness for Mechanism Design

first draftThe currently prevailing equilibrium-based approach to mechanism design suffers from a plurality of fundamental problems, and new conceptual frameworks are needed to solve or sufficiently alleviate them. In this paper, we put forward rational robustness, a new solution concept/implementation notion that is not equilibrium-based; prove its fundamental structural theorems; and compare it with prior notions. Our notion of implementation is specifically built so as to be robust against the problem of equilibrium selection. We prove it robust against other fundamental problems as well in different papers.Work partially supported by ONR Contract Number N00014-09-1-0597