On Revenue Maximization with Sharp Multi-Unit Demands

We consider markets consisting of a set of indivisible items, and buyers that have {\em sharp} multi-unit demand. This means that each buyer $i$ wants a specific number $d_i$ of items; a bundle of size less than $d_i$ has no value, while a bundle of size greater than $d_i$ is worth no more than the most valued $d_i$ items (valuations being additive). We consider the objective of setting prices and allocations in order to maximize the total revenue of the market maker. The pricing problem with sharp multi-unit demand buyers has a number of properties that the unit-demand model does not possess, and is an important question in algorithmic pricing. We consider the problem of computing a revenue maximizing solution for two solution concepts: competitive equilibrium and envy-free pricing. For unrestricted valuations, these problems are NP-complete; we focus on a realistic special case of "correlated values" where each buyer $i$ has a valuation v_i\qual_j for item $j$, where $v_i$ and \qual_j are positive quantities associated with buyer $i$ and item $j$ respectively. We present a polynomial time algorithm to solve the revenue-maximizing competitive equilibrium problem. For envy-free pricing, if the demand of each buyer is bounded by a constant, a revenue maximizing solution can be found efficiently; the general demand case is shown to be NP-hard.Comment: page2

Budget Constrained Auctions with Heterogeneous Items

In this paper, we present the first approximation algorithms for the problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders can have arbitrary demand and budget constraints. Our mechanisms are surprisingly simple: We show that a sequential all-pay mechanism is a 4 approximation to the revenue of the optimal ex-interim truthful mechanism with discrete correlated type space for each bidder. We also show that a sequential posted price mechanism is a O(1) approximation to the revenue of the optimal ex-post truthful mechanism when the type space of each bidder is a product distribution that satisfies the standard hazard rate condition. We further show a logarithmic approximation when the hazard rate condition is removed, and complete the picture by showing that achieving a sub-logarithmic approximation, even for regular distributions and one bidder, requires pricing bundles of items. Our results are based on formulating novel LP relaxations for these problems, and developing generic rounding schemes from first principles. We believe this approach will be useful in other Bayesian mechanism design contexts.Comment: Final version accepted to STOC '10. Incorporates significant reviewer comment

The Value of Information Concealment

We consider a revenue optimizing seller selling a single item to a buyer, on whose private value the seller has a noisy signal. We show that, when the signal is kept private, arbitrarily more revenue could potentially be extracted than if the signal is leaked or revealed. We then show that, if the seller is not allowed to make payments to the buyer, the gap between the two is bounded by a multiplicative factor of 3, if the value distribution conditioning on each signal is regular. We give examples showing that both conditions are necessary for a constant bound to hold. We connect this scenario to multi-bidder single-item auctions where bidders' values are correlated. Similarly to the setting above, we show that the revenue of a Bayesian incentive compatible, ex post individually rational auction can be arbitrarily larger than that of a dominant strategy incentive compatible auction, whereas the two are no more than a factor of 5 apart if the auctioneer never pays the bidders and if each bidder's value conditioning on the others' is drawn according to a regular distribution. The upper bounds in both settings degrade gracefully when the distribution is a mixture of a small number of regular distributions

De facto capital mobility, equality, and tax policy in open economies

This paper attempts at giving theoretical and empirical answers to the remaining puzzles in the literature on tax competition: the persistently high tax rates on mobile capital and the large variation in domestic tax systems. I argue that governments face a political trilemma, in which they cannot maintain the politically optimal level of public good provision, reduce capital taxes to competitive levels and implement a political support-maximizing mix of tax rates on capital and labour simultaneously. In particular, while legal restriction on capital flows have been eliminated by virtually all OECD countries, de facto capital mobility falls short of being perfect. Limits to full capital mobility result from ownership structures: the higher the concentration of capital, the higher the de facto mobility of capital and the lower the equilibrium tax rate. Second, the demand for the provision of public goods further constraints governments’ choices of the capital tax rate. If revenue from taxation of mobile factors declines, politicians cannot necessarily cut back spending without losing political support. Policy makers, accordingly, do not face a simple optimization problem when deciding on capital taxation. Rather, they have to choose a tax system which allows them to supply an appropriate level of public goods. Policy makers finally face a trade-off resulting from the redistributive conflict between capital-owners and workers. This conflict does not resemble a mere zero-sum game, because lower levels of capital taxation are likely to improve aggregate welfare, but the decision on capital taxation also cannot be analyzed in isolation from the distributive effects of reducing taxes on mobile factors. This political logic of tax competition generates important predictions which are tested empirically for 23 OECD countries over 30 years within a spatial econometrics framework

"Big Bang" Versus Gradualism in Economic Reforms: An Intertemporal Analysis with an Application to China

This paper analyzes issues concerning the speed of adjustment and sequencing of reforms in a transition economy. It presents a dynamic general equilibrium model parameterized with Chinese data. The model is used to generate different policy simulations that highlight the importance of the policy instruments used during the transition period. The simulations consider privatization, tariff reform, and devaluation, as well as alternative speeds of introducing these policies. They show that different speeds of adjustment, as well as sequencing of reforms, will have very different implications for macroeconomic aggregates. Copyright 2003, International Monetary Fund

Preemptive Scheduling of EV Charging for Providing Demand Response Services

We develop a new algorithm for scheduling the charging process of a large number of electric vehicles (EVs) over a finite horizon. We assume that EVs arrive at the charging stations with different charge levels and different flexibility windows. The arrival process is assumed to have a known distribution and that the charging process of EVs can be preemptive. We pose the scheduling problem as a dynamic program with constraints. We show that the resulting formulation leads to a monotone dynamic program with Lipschitz continuous value functions that are robust against perturbation of system parameters. We propose a simulation based fitted value iteration algorithm to determine the value function approximately, and derive the sample complexity for computing the approximately optimal solution.Comment: 21 pages, submitted to SEGA

State and Local Fiscal Behavior and Federal Grant Policy

macroeconomics, federal grant policy, state fiscal, local fiscal