Optimal Income Taxation, Public-Goods Provision and Public-Sector Pricing: A Contribution to the Foundations of Public Economics

The paper develops an integrated model of optimal nonlinear income taxation, public-goods provision and pricing in a large economy. With asymmetric information about labour productivities and publicgoods preferences, the multidimensional mechanism design problem becomes tractable by requiring renegotiation proofness of the final allocation of private goods and admission tickets for excludable public goods. Under an affiliation assumption on the underlying distribution, optimal income taxation, public-goods provision and admission fees have the same qualitative properties as in unidimensional models. These properties are obtained for utilitarian welfare maximization and for a Ramsey-Boiteux formulation with interim participation constraints.Optimal Income Taxation, Public Goods, Public-Sector Pricing, Multidimensional Mechanism Design, Ramsey-Boiteux Pricing

Optimal Income Taxation, Public-Goods Provision

The paper develops an integrated model of optimal nonlinear income taxation, public-goods provision and pricing in a large economy. With asymmetric information about labour productivities and publicgoods preferences, the multidimensional mechanism design problem becomes tractable by requiring renegotiation proofness of the final allocation of private goods and admission tickets for excludable public goods. Under an affiliation assumption on the underlying distribution, optimal income taxation, public-goods provision and admission fees have the same qualitative properties as in unidimensional models. These properties are obtained for utilitarian welfare maximization and for a Ramsey-Boiteux formulation with interim participation constraints.

Optimal Design of Robust Combinatorial Mechanisms for Substitutable Goods

In this paper we consider multidimensional mechanism design problem for selling discrete substitutable items to a group of buyers. Previous work on this problem mostly focus on stochastic description of valuations used by the seller. However, in certain applications, no prior information regarding buyers' preferences is known. To address this issue, we consider uncertain valuations and formulate the problem in a robust optimization framework: the objective is to minimize the maximum regret. For a special case of revenue-maximizing pricing problem we present a solution method based on mixed-integer linear programming formulation

Near-Optimal and Robust Mechanism Design for Covering Problems with Correlated Players

We consider the problem of designing incentive-compatible, ex-post individually rational (IR) mechanisms for covering problems in the Bayesian setting, where players' types are drawn from an underlying distribution and may be correlated, and the goal is to minimize the expected total payment made by the mechanism. We formulate a notion of incentive compatibility (IC) that we call {\em support-based IC} that is substantially more robust than Bayesian IC, and develop black-box reductions from support-based-IC mechanism design to algorithm design. For single-dimensional settings, this black-box reduction applies even when we only have an LP-relative {\em approximation algorithm} for the algorithmic problem. Thus, we obtain near-optimal mechanisms for various covering settings including single-dimensional covering problems, multi-item procurement auctions, and multidimensional facility location.Comment: Major changes compared to the previous version. Please consult this versio

Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study

Optimal procurement mechanism with observable quality

In a procurement contract the Administration usually has some prior information about the quality of the bidding firms. The goal of this article is to characterize the optimal mechanism in such a situation, when firms have private information about their costs. The optimal mechanism selects low-quality firms more often than it would be efficient with perfect information. We also compare this mechanism with others frequently used by the Spanish Administration such as the first price sealed bid auction and the previous admission auction

Bounding the Optimal Revenue of Selling Multiple Goods

Using duality theory techniques we derive simple, closed-form formulas for bounding the optimal revenue of a monopolist selling many heterogeneous goods, in the case where the buyer's valuations for the items come i.i.d. from a uniform distribution and in the case where they follow independent (but not necessarily identical) exponential distributions. We apply this in order to get in both these settings specific performance guarantees, as functions of the number of items $m$, for the simple deterministic selling mechanisms studied by Hart and Nisan [EC 2012], namely the one that sells the items separately and the one that offers them all in a single bundle. We also propose and study the performance of a natural randomized mechanism for exponential valuations, called Proportional. As an interesting corollary, for the special case where the exponential distributions are also identical, we can derive that offering the goods in a single full bundle is the optimal selling mechanism for any number of items. To our knowledge, this is the first result of its kind: finding a revenue-maximizing auction in an additive setting with arbitrarily many goods