2,518 research outputs found
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 wants a
specific number of items; a bundle of size less than has no value,
while a bundle of size greater than is worth no more than the most valued
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 has a
valuation v_i\qual_j for item , where and \qual_j are positive
quantities associated with buyer and item 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
Quadratic Regularization of Unit-Demand Envy-Free Pricing Problems and Application to Electricity Markets
We consider a profit-maximizing model for pricing contracts as an extension
of the unit-demand envy-free pricing problem: customers aim to choose a
contract maximizing their utility based on a reservation bill and multiple
price coefficients (attributes). A classical approach supposes that the
customers have deterministic utilities; then, the response of each customer is
highly sensitive to price since it concentrates on the best offer. A second
approach is to consider logit model to add a probabilistic behavior in the
customers' choices. To circumvent the intrinsic instability of the former and
the resolution difficulties of the latter, we introduce a quadratically
regularized model of customer's response, which leads to a quadratic program
under complementarity constraints (QPCC). This allows to robustify the
deterministic model, while keeping a strong geometrical structure. In
particular, we show that the customer's response is governed by a polyhedral
complex, in which every polyhedral cell determines a set of contracts which is
effectively chosen. Moreover, the deterministic model is recovered as a limit
case of the regularized one. We exploit these geometrical properties to develop
an efficient pivoting heuristic, which we compare with implicit or non-linear
methods from bilevel programming. These results are illustrated by an
application to the optimal pricing of electricity contracts on the French
market.Comment: 37 pages, 9 figures; adding a section on the pricing of electricity
contract
Cooperation and equity in the river sharing problem
This paper considers environments in which several agents (countries, farmers, cities) share water from a river. Each agent enjoys a concave benefit function from consuming water up to a satiation level. Noncooperative extraction is typically inefficient and any group of agents can gain if they agree on how to allocate water with monetary compensations. The paper describes which allocations of water and money are acceptable to riparian agents according to core stability and several criteria of fairness. It reviews some theoretical results. It then discusses the implementation of the proposed allocation with negotiation rules and in water markets. Lastly, it provides some policy insights.WATER ALLOCATION;GAME;CORE;WATER MARKET;NEGOTIATION;RULES;EXTERNALITIES
INSTITUTIONAL ARRANGEMENTS FOR MANAGING WATER CONFLICTS IN MINNESOTA
Resource /Energy Economics and Policy,
Graph Pricing Problem on Bounded Treewidth, Bounded Genus and k-partite graphs
Consider the following problem. A seller has infinite copies of products
represented by nodes in a graph. There are consumers, each has a budget and
wants to buy two products. Consumers are represented by weighted edges. Given
the prices of products, each consumer will buy both products she wants, at the
given price, if she can afford to. Our objective is to help the seller price
the products to maximize her profit.
This problem is called {\em graph vertex pricing} ({\sf GVP}) problem and has
resisted several recent attempts despite its current simple solution. This
motivates the study of this problem on special classes of graphs. In this
paper, we study this problem on a large class of graphs such as graphs with
bounded treewidth, bounded genus and -partite graphs.
We show that there exists an {\sf FPTAS} for {\sf GVP} on graphs with bounded
treewidth. This result is also extended to an {\sf FPTAS} for the more general
{\em single-minded pricing} problem. On bounded genus graphs we present a {\sf
PTAS} and show that {\sf GVP} is {\sf NP}-hard even on planar graphs.
We study the Sherali-Adams hierarchy applied to a natural Integer Program
formulation that -approximates the optimal solution of {\sf GVP}.
Sherali-Adams hierarchy has gained much interest recently as a possible
approach to develop new approximation algorithms. We show that, when the input
graph has bounded treewidth or bounded genus, applying a constant number of
rounds of Sherali-Adams hierarchy makes the integrality gap of this natural
{\sf LP} arbitrarily small, thus giving a -approximate solution
to the original {\sf GVP} instance.
On -partite graphs, we present a constant-factor approximation algorithm.
We further improve the approximation factors for paths, cycles and graphs with
degree at most three.Comment: Preprint of the paper to appear in Chicago Journal of Theoretical
Computer Scienc
- …