Bayesian Incentive Compatibility via Fractional Assignments

Bei, Xiaohui; Huang, Zhiyi

doi:10.1137/1.9781611973082.57

Cited by 51 publications

(94 citation statements)

References 22 publications

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“…Our results stand in contrast to existing constructions in Bayesian mechanism design [12,11,4]. In that prior work, it was shown that general black-box reductions for social welfare exist in a Bayesian setting, where the input is drawn from a commonly known distribution F and the optimization and incentive compatibility requirements are with respect to F. Our first result demonstrates that no such reduction is possible when the solution concept is ex post incentive compatibility (i.e.…”

Section: Introductioncontrasting

confidence: 66%

“…Since the mechanism is meant to be "black-box," we will require that it can only output an allocation that it has observed while querying the algorithm at different vectors 4 . This last property is crucial in our constructions and allows us to "hide" good allocations from the transformation.…”

Section: Our Results and Techniquesmentioning

confidence: 99%

“…Much recent research has focused on generalizing such reductions to encompass approximation algorithms. Recently, striking positive results have been obtained for many important cases, especially single-parameter problems, in both Bayesian [12,11,4] and ex post (i.e. non-Bayesian) [15,3,8,10,14] settings.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the limits of black-box reductions in mechanism design

Chawla

Immorlica

Lucier

2012

Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing

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We consider the problem of converting an arbitrary approximation algorithm for a single-parameter optimization problem into a computationally efficient truthful mechanism. We ask for reductions that are black-box, meaning that they require only oracle access to the given algorithm and in particular do not require explicit knowledge of the problem constraints. Such a reduction is known to be possible, for example, for the social welfare objective when the goal is to achieve Bayesian truthfulness and preserve social welfare in expectation. We show that a black-box reduction for the social welfare objective is not possible if the resulting mechanism is required to be truthful in expectation and to preserve the worst-case approximation ratio of the algorithm to within a subpolynomial factor. Further, we prove that for other objectives such as makespan, no black-box reduction is possible even if we only require Bayesian truthfulness and an average-case performance guarantee.

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Section: Introductioncontrasting

confidence: 66%

Section: Our Results and Techniquesmentioning

confidence: 99%

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On the limits of black-box reductions in mechanism design

Chawla

Immorlica

Lucier

2012

Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing

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“…For the relaxation of the problem where only approximate incentive compatibility is required, Bei and Huang (2011) solve the case of multi-dimensional agents with discrete type space, and Hartline et al (2011 solve the general case. These reductions are approximation schemes that are polynomial in the number of agents, the desired approximation factor, and a measure of the size of the agents' type spaces (e.g., its dimension).…”

Section: A Bayesian Incentive Compatible Black-box Reductionmentioning

confidence: 99%

Bernoulli factories and black-box reductions in mechanism design

Dughmi

Hartline

Kleinberg

et al. 2017

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

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We provide a polynomial time reduction from Bayesian incentive compatible mechanism design to Bayesian algorithm design for welfare maximization problems. Unlike prior results, our reduction achieves exact incentive compatibility for problems with multi-dimensional and continuous type spaces.The key technical barrier preventing exact incentive compatibility in prior black-box reductions is that repairing violations of incentive constraints requires understanding the distribution of the mechanism's output, which is typically #P-hard to compute. Reductions that instead estimate the output distribution by sampling inevitably suffer from sampling error, which typically precludes exact incentive compatibility.We overcome this barrier by employing and generalizing the computational model in the literature on Bernoulli Factories. In a Bernoulli factory problem, one is given a function mapping the bias of an "input coin" to that of an "output coin", and the challenge is to efficiently simulate the output coin given only sample access to the input coin. Consider a generalization which we call the expectations from samples computational model, in which a problem instance is specified by a function mapping the expected values of a set of input distributions to a distribution over outcomes. The challenge is to give a polynomial time algorithm that exactly samples from the distribution over outcomes given only sample access to the input distributions.In this model, we give a polynomial time algorithm for the function given by exponential weights: expected values of the input distributions correspond to the weights of alternatives and we wish to select an alternative with probability proportional to an exponential function of its weight. This algorithm is the key ingredient in designing an incentive compatible mechanism for bipartite matching, which can be used to make the approximately incentive compatible reduction of exactly incentive compatible.

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“…Once the leap to the Bayesian setting is made the goal is typically this: Design a BIC, possibly randomized, mechanism whose expected revenue is optimal among all BIC, possibly randomized, mechanisms. 2 One of the most celebrated results in this realm is Myerson's optimal auction [19], which achieves optimal revenue via an elegant design that spans several important settings. Despite its significance, Myerson's result is limited to the case where bidders are single-dimensional.…”

Section: Introductionmentioning

confidence: 99%

On optimal multidimensional mechanism design

2011

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We efficiently solve the optimal multi-dimensional mechanism design problem for independent bidders with arbitrary demand constraints when either the number of bidders is a constant or the number of items is a constant. In the first setting, we need that each bidder's values for the items are sampled from a possibly correlated, item-symmetric distribution, allowing different distributions for each bidder. In the second setting, we allow the values of each bidder for the items to be arbitrarily correlated, but assume that the distribution of bidder types is bidder-symmetric. These symmetric distributions include i.i.d. distributions, as well as many natural correlated distributions. E.g., an item-symmetric distribution can be obtained by taking an arbitrary distribution, and "forgetting" the names of items; this could arise when different members of a bidder population have various sorts of correlations among the items, but the items are "the same" with respect to a random bidder from the population.For all > 0, we obtain a computationally efficient additive -approximation, when the value distributions are bounded, or a multiplicative (1− )-approximation when the value distributions are unbounded, but satisfy the Monotone Hazard Rate condition, covering a widely studied class of distributions in Economics. Our running time is polynomial in max{#items,#bidders}, and not the size of the support of the joint distribution of all bidders' values for all items, which is typically exponential in both the number of items and the number of bidders. Our mechanisms are randomized, explicitly price bundles, and in some cases can also accommodate budget constraints.Our results are enabled by establishing several new tools and structural properties of Bayesian mechanisms. In particular, we provide a symmetrization technique that turns any truthful mechanism into one that has the same revenue and respects all symmetries in the underlying value distributions. We also prove that item-symmetric mechanisms satisfy a natural strong-monotonicity property which, unlike cyclic-monotonicity, can be harnessed algorithmically. Finally, we provide a technique that turns any given -BIC mechanism (i.e. one where incentive constraints are violated by ) into a truly-BIC mechanism at the cost of O( √ ) revenue. We expect our tools to be used beyond the settings we consider here. Indeed there has already been follow-up research [8,9] making use of our tools.

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Bayesian Incentive Compatibility via Fractional Assignments

Cited by 51 publications

References 22 publications

On the limits of black-box reductions in mechanism design

On the limits of black-box reductions in mechanism design

Bernoulli factories and black-box reductions in mechanism design

On optimal multidimensional mechanism design

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