17,041 research outputs found

    Mechanism Design for Fair Allocation

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    Mechanism design for a social utility being the sum of agents' utilities (SoU) is a well-studied problem. There are, however, a number of problems of theoretical and practical interest where a designer may have a different objective than maximization of the SoU. One motivation for this is the desire for more equitable allocation of resources among agents. A second, more subtle, motivation is the fact that a fairer allocation indirectly implies less variation in taxes which can be desirable in a situation where (implicit) individual agent budgetary constraints make payment of large taxes unrealistic. In this paper we study a family of social utilities that provide fair allocation (with SoU being subsumed as an extreme case) and derive conditions under which Bayesian and Dominant strategy implementation is possible. Furthermore, it is shown how a simple modification of the above mechanism can guarantee full Bayesian implementation. Through a numerical example it is shown that the proposed method can result in significant gains both in allocation fairness and tax reduction

    Allocative and Informational Externalities in Auctions and Related Mechanisms

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    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

    Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systems

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    We propose a novel decomposition framework for the distributed optimization of general nonconvex sum-utility functions arising naturally in the system design of wireless multiuser interfering systems. Our main contributions are: i) the development of the first class of (inexact) Jacobi best-response algorithms with provable convergence, where all the users simultaneously and iteratively solve a suitably convexified version of the original sum-utility optimization problem; ii) the derivation of a general dynamic pricing mechanism that provides a unified view of existing pricing schemes that are based, instead, on heuristics; and iii) a framework that can be easily particularized to well-known applications, giving rise to very efficient practical (Jacobi or Gauss-Seidel) algorithms that outperform existing adhoc methods proposed for very specific problems. Interestingly, our framework contains as special cases well-known gradient algorithms for nonconvex sum-utility problems, and many blockcoordinate descent schemes for convex functions.Comment: submitted to IEEE Transactions on Signal Processin

    Travel Demand Model with Heterogeneous Users and Endogenous Congestion: An application to optimal pricing of bus services

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    We formulate and estimate a structural model for travel demand, in which users have hetero- geneous preferences and make their transport decisions considering the network congestion. A key component in the model is that users have incomplete information about the preferences of other users in the network and they behave strategically when they make transportation decisions (mode and number of trips). Therefore, the congestion level is endogenously determinate in the equilibrium of the game played by users. For the estimation, we use the first order conditions of the users' utility maximization problem to derive the likelihood function and apply Bayesian methods for inference. Using data from Santiago, Chile, the estimated demand elasticities are consistent with results reported in the literature and the parameters confirm the effect of the congestion on the individuals' preferences. Finally, we compute optimal nonlinear prices for buses in Santiago, Chile. As a result, the nonlinear pricing schedule produces total benefits slightly greater than the linear pricing. Also, nonlinear pricing implies fewer individuals making trips by bus, but a higher number of trips per individual.

    Optimal Dynamic Taxes

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    We study optimal labor and savings distortions in a lifecycle model with idiosyncratic shocks. We show a tight connection between its recursive formulation and a static Mirrlees model with two goods, which allows us to derive elasticity-based expressions for the dynamic optimal distortions. We derive a generalization of a savings distortion for non-separable preferences and show that, under certain conditions, the labor wedge tends to zero for sufficiently high skills. We estimate skill distributions using individual data on the U.S. taxes and labor incomes. Computed optimal distortions decrease for sufficiently high incomes and increase with age.

    Budget Feasible Mechanisms for Experimental Design

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    In the classical experimental design setting, an experimenter E has access to a population of nn potential experiment subjects i∈{1,...,n}i\in \{1,...,n\}, each associated with a vector of features xi∈Rdx_i\in R^d. Conducting an experiment with subject ii reveals an unknown value yi∈Ry_i\in R to E. E typically assumes some hypothetical relationship between xix_i's and yiy_i's, e.g., yi≈βxiy_i \approx \beta x_i, and estimates β\beta from experiments, e.g., through linear regression. As a proxy for various practical constraints, E may select only a subset of subjects on which to conduct the experiment. We initiate the study of budgeted mechanisms for experimental design. In this setting, E has a budget BB. Each subject ii declares an associated cost ci>0c_i >0 to be part of the experiment, and must be paid at least her cost. In particular, the Experimental Design Problem (EDP) is to find a set SS of subjects for the experiment that maximizes V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i}) under the constraint ∑i∈Sci≤B\sum_{i\in S}c_i\leq B; our objective function corresponds to the information gain in parameter β\beta that is learned through linear regression methods, and is related to the so-called DD-optimality criterion. Further, the subjects are strategic and may lie about their costs. We present a deterministic, polynomial time, budget feasible mechanism scheme, that is approximately truthful and yields a constant factor approximation to EDP. In particular, for any small δ>0\delta > 0 and ϵ>0\epsilon > 0, we can construct a (12.98, ϵ\epsilon)-approximate mechanism that is δ\delta-truthful and runs in polynomial time in both nn and log⁡log⁡Bϵδ\log\log\frac{B}{\epsilon\delta}. We also establish that no truthful, budget-feasible algorithms is possible within a factor 2 approximation, and show how to generalize our approach to a wide class of learning problems, beyond linear regression
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