11,995 research outputs found
Online Learning and Profit Maximization from Revealed Preferences
We consider the problem of learning from revealed preferences in an online
setting. In our framework, each period a consumer buys an optimal bundle of
goods from a merchant according to her (linear) utility function and current
prices, subject to a budget constraint. The merchant observes only the
purchased goods, and seeks to adapt prices to optimize his profits. We give an
efficient algorithm for the merchant's problem that consists of a learning
phase in which the consumer's utility function is (perhaps partially) inferred,
followed by a price optimization step. We also consider an alternative online
learning algorithm for the setting where prices are set exogenously, but the
merchant would still like to predict the bundle that will be bought by the
consumer for purposes of inventory or supply chain management. In contrast with
most prior work on the revealed preferences problem, we demonstrate that by
making stronger assumptions on the form of utility functions, efficient
algorithms for both learning and profit maximization are possible, even in
adaptive, online settings
Social welfare and profit maximization from revealed preferences
Consider the seller's problem of finding optimal prices for her
(divisible) goods when faced with a set of consumers, given that she can
only observe their purchased bundles at posted prices, i.e., revealed
preferences. We study both social welfare and profit maximization with revealed
preferences. Although social welfare maximization is a seemingly non-convex
optimization problem in prices, we show that (i) it can be reduced to a dual
convex optimization problem in prices, and (ii) the revealed preferences can be
interpreted as supergradients of the concave conjugate of valuation, with which
subgradients of the dual function can be computed. We thereby obtain a simple
subgradient-based algorithm for strongly concave valuations and convex cost,
with query complexity , where is the additive
difference between the social welfare induced by our algorithm and the optimum
social welfare. We also study social welfare maximization under the online
setting, specifically the random permutation model, where consumers arrive
one-by-one in a random order. For the case where consumer valuations can be
arbitrary continuous functions, we propose a price posting mechanism that
achieves an expected social welfare up to an additive factor of
from the maximum social welfare. Finally, for profit maximization (which may be
non-convex in simple cases), we give nearly matching upper and lower bounds on
the query complexity for separable valuations and cost (i.e., each good can be
treated independently)
Monopolistic Competition, International Trade and Firm Heterogeneity - a Life Cycle Perspective
This paper presents a dynamic international trade model based on monopolistic competition, where observed intra-industry differences at a given point in time reflect different stages of the firmâs life cycle. New product varieties of still higher quality enter the market every period rendering old varieties obsolescent in a process of creative destruction. For given technology (variety) production costs decrease after an infant period due to learning. It is shown that several patterns of exports may arise depending primarily on the size of fixed trade costs. At a given point in time firms therefore differ due to different age, although all firms are symmetric in a life cycle perspective. The paper thus offers an alternative view on firm heterogeneity compared with other recent papers, where productivity differences appear as an outcome of a stochastic process.Product innovations; learning; creative destruction; firm heterogeneity; export performance
Social Preferences, Skill Segregation and Wage Dynamics
We study the earning structure and the equilibrium asignment of workers to firms in a model in which workers have social preferences, and skills are perfectly substitutable in production. Firms offer long-term contracts, and we allow for frictions in the labour market in the form of mobility costs. The model delivers specific predictions about the nature of worker flows, about the characteristic of workplace skill segregation, and about wage dispersion both within and cross firms. We shows that long-term contracts in the resence of social preferences associate within-firm wage dispersion with novel "internal labour market" features such as gradual promotions, productivity-unrelated wage increases, and downward wage flexibility. These three dynamic features lead to productivity-unrelated wage volatily within firms.Publicad
A General Theory of Sample Complexity for Multi-Item Profit Maximization
The design of profit-maximizing multi-item mechanisms is a notoriously
challenging problem with tremendous real-world impact. The mechanism designer's
goal is to field a mechanism with high expected profit on the distribution over
buyers' values. Unfortunately, if the set of mechanisms he optimizes over is
complex, a mechanism may have high empirical profit over a small set of samples
but low expected profit. This raises the question, how many samples are
sufficient to ensure that the empirically optimal mechanism is nearly optimal
in expectation? We uncover structure shared by a myriad of pricing, auction,
and lottery mechanisms that allows us to prove strong sample complexity bounds:
for any set of buyers' values, profit is a piecewise linear function of the
mechanism's parameters. We prove new bounds for mechanism classes not yet
studied in the sample-based mechanism design literature and match or improve
over the best known guarantees for many classes. The profit functions we study
are significantly different from well-understood functions in machine learning,
so our analysis requires a sharp understanding of the interplay between
mechanism parameters and buyer values. We strengthen our main results with
data-dependent bounds when the distribution over buyers' values is
"well-behaved." Finally, we investigate a fundamental tradeoff in sample-based
mechanism design: complex mechanisms often have higher profit than simple
mechanisms, but more samples are required to ensure that empirical and expected
profit are close. We provide techniques for optimizing this tradeoff
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