8 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
Heterogeneous Facility Location without Money
The study of the facility location problem in the presence of self-interested agents has recently emerged as the benchmark problem in the research on mechanism design without money. In the setting studied in the literature so far, agents are single-parameter in that their type is a single number encoding their position on a real line. We here initiate a more realistic model for several real-life scenarios. Specifically, we propose and analyze heterogeneous facility location without money, a novel model wherein: (i) we have multiple heterogeneous (i.e., serving different purposes) facilities, (ii) agents' locations are disclosed to the mechanism and (iii) agents bid for the set of facilities they are interested in (as opposed to bidding for their position on the network).
We study the heterogeneous facility location problem under two different objective functions, namely: social cost (i.e., sum of all agents' costs) and maximum cost. For either objective function, we study the approximation ratio of both deterministic and randomized truthful algorithms under the simplifying assumption that the underlying network topology is a line. For the social cost objective function, we devise an (n-1)-approximate deterministic truthful mechanism and prove a constant approximation lower bound. Furthermore, we devise an optimal and truthful (in expectation) randomized algorithm. As regards the maximum cost objective function, we propose a 3-approximate deterministic strategyproof algorithm, and prove a 3/2 approximation lower bound for deterministic strategyproof mechanisms. Furthermore, we propose a 3/2-approximate randomized strategyproof algorithm and prove a 4/3 approximation lower bound for randomized strategyproof algorithms
Combinatorial Auctions without Money
Algorithmic Mechanism Design attempts to marry computation and incentives, mainly by leveraging monetary transfers between designer and selfish agents involved. This is principally because in absence of money, very little can be done to enforce truthfulness. However, in certain applications, money is unavailable, morally unacceptable or might simply be at odds with the objective of the mechanism. For example, in Combinatorial Auctions (CAs), the paradigmatic problem of the area, we aim at solutions of maximum social welfare, but still charge the society to ensure truthfulness. We focus on the design of incentive-compatible CAs without money in the general setting of k-minded bidders. We trade monetary transfers with the observation that the mechanism can detect certain lies of the bidders: i.e., we study truthful CAs with verification and without money. In this setting, we characterize the class of truthful mechanisms and give a host of upper and lower bounds on the approximation ratio obtained by either deterministic or randomized truthful mechanisms. Our results provide an almost complete picture of truthfully approximating CAs in this general setting with multi-dimensional bidders
Mechanisms for fair allocation problems: no-punishment payment rules in verifiable settings
Mechanism design is considered in the context of fair allocations of indivisible goods with monetary compensation, by focusing on problems where agents' declarations on allocated goods can be verified before payments are performed. A setting is considered where verification might be subject to errors, so that payments have to be awarded under the presumption of innocence, as incorrect declared values do not necessarily mean manipulation attempts by the agents. Within this setting, a mechanism is designed that is shown to be truthful, efficient, and budget-balanced. Moreover, agents' utilities are fairly determined by the Shapley value of suitable coalitional games, and enjoy highly desirable properties such as equal treatment of equals, envy-freeness, and a stronger one called individual-optimality. In particular, the latter property guarantees that, for every agent, her/his utility is the maximum possible one over any alternative optimal allocation.
The computational complexity of the proposed mechanism is also studied. It turns out that it is #P-complete so that, to deal with applications with many agents involved, two polynomial-time randomized variants are also proposed: one that is still truthful and efficient, and which is approximately budget-balanced with high probability, and another one that is truthful in expectation, while still budget-balanced and efficient