118 research outputs found
Implementation in Advised Strategies: Welfare Guarantees from Posted-Price Mechanisms When Demand Queries Are NP-Hard
State-of-the-art posted-price mechanisms for submodular bidders with
items achieve approximation guarantees of [Assadi and
Singla, 2019]. Their truthfulness, however, requires bidders to compute an
NP-hard demand-query. Some computational complexity of this form is
unavoidable, as it is NP-hard for truthful mechanisms to guarantee even an
-approximation for any [Dobzinski and
Vondr\'ak, 2016]. Together, these establish a stark distinction between
computationally-efficient and communication-efficient truthful mechanisms.
We show that this distinction disappears with a mild relaxation of
truthfulness, which we term implementation in advised strategies, and that has
been previously studied in relation to "Implementation in Undominated
Strategies" [Babaioff et al, 2009]. Specifically, advice maps a tentative
strategy either to that same strategy itself, or one that dominates it. We say
that a player follows advice as long as they never play actions which are
dominated by advice. A poly-time mechanism guarantees an -approximation
in implementation in advised strategies if there exists poly-time advice for
each player such that an -approximation is achieved whenever all
players follow advice. Using an appropriate bicriterion notion of approximate
demand queries (which can be computed in poly-time), we establish that (a
slight modification of) the [Assadi and Singla, 2019] mechanism achieves the
same -approximation in implementation in advised
strategies
Approaching Utopia: Strong Truthfulness and Externality-Resistant Mechanisms
We introduce and study strongly truthful mechanisms and their applications.
We use strongly truthful mechanisms as a tool for implementation in undominated
strategies for several problems,including the design of externality resistant
auctions and a variant of multi-dimensional scheduling
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
Combinatorial Voting
We study elections that simultaneously decide multiple issues, where voters have independent private values over bundles of issues. The innovation is in considering nonseparable preferences, where issues may be complements or substitutes. Voters face a political exposure problem: the optimal vote for a particular issue will depend on the resolution of the other issues. Moreover, the probabilities that the other issues will pass should be conditioned on being pivotal. We prove that equilibrium exists when distributions over values have full support or when issues are complements. We then study large elections with two issues. There exists a nonempty open set of distributions where the probability of either issue passing fails to converge to either 1 or 0 for all limit equilibria. Thus, the outcomes of large elections are not generically predictable with independent private values, despite the fact that there is no aggregate uncertainty regarding fundamentals. While the Condorcet winner is not necessarily the outcome of a multi-issue election, we provide sufficient conditions that guarantee the implementation of the Condorcet winner. © 2012 The Econometric Society
Resilient Knowledge-Based Mechanisms For Truly Combinatorial Auctions (And Implementation in Surviving Strategies)
We put forward a new mechanism achieving a high benchmark for (both revenue and) the sum of revenue and efficiency in truly combinatorial auctions. Notably, our mechanism guarantees its performance (1) in a very adversarial collusion model; (2) for any profile of strategies surviving the iterated elimination of dominated strategies; and (3) by leveraging the knowledge that the players have about each other (in a non-Bayesian setting).Our mechanism also is computationally efficient, and preserves the players' privacy to an unusual extent
Mechanism Design With Approximate Player Types
We investigate mechanism design when the players do not exactly know their types, but have instead only partial information about them
Mechanism Design with Set-Theoretic Beliefs
In settings of incomplete information, we put forward (1) a very conservative -- indeed, purely set-theoretic -- model of the beliefs (including totally wrong ones) that each player may have about the payoff types of his opponents, and (2) a new and robust solution concept, based on mutual belief of rationality, capable of leveraging such conservative beliefs. We exemplify the applicability of our new approach for single-good auctions, by showing that, under our solution concept, a normal-form, simple, and deterministic mechanism guarantees -- up to an arbitrarily small, additive constant -- a revenue benchmark that is always greater than or equal to the second-highest valuation, and sometimes much greater. By contrast, we also prove that the same benchmark cannot even be approximated within any positive factor, under classical solution concepts.United States. Office of Naval Research (Grant number N00014-09-1-0597
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