4,972 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
Campaign Management under Approval-Driven Voting Rules
Approval-like voting rules, such as Sincere-Strategy Preference-Based
Approval voting (SP-AV), the Bucklin rule (an adaptive variant of -Approval
voting), and the Fallback rule (an adaptive variant of SP-AV) have many
desirable properties: for example, they are easy to understand and encourage
the candidates to choose electoral platforms that have a broad appeal. In this
paper, we investigate both classic and parameterized computational complexity
of electoral campaign management under such rules. We focus on two methods that
can be used to promote a given candidate: asking voters to move this candidate
upwards in their preference order or asking them to change the number of
candidates they approve of. We show that finding an optimal campaign management
strategy of the first type is easy for both Bucklin and Fallback. In contrast,
the second method is computationally hard even if the degree to which we need
to affect the votes is small. Nevertheless, we identify a large class of
scenarios that admit fixed-parameter tractable algorithms.Comment: 34 pages, 1 figur
Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks
Finding actions that satisfy the constraints imposed by both external inputs
and internal representations is central to decision making. We demonstrate that
some important classes of constraint satisfaction problems (CSPs) can be solved
by networks composed of homogeneous cooperative-competitive modules that have
connectivity similar to motifs observed in the superficial layers of neocortex.
The winner-take-all modules are sparsely coupled by programming neurons that
embed the constraints onto the otherwise homogeneous modular computational
substrate. We show rules that embed any instance of the CSPs planar four-color
graph coloring, maximum independent set, and Sudoku on this substrate, and
provide mathematical proofs that guarantee these graph coloring problems will
convergence to a solution. The network is composed of non-saturating linear
threshold neurons. Their lack of right saturation allows the overall network to
explore the problem space driven through the unstable dynamics generated by
recurrent excitation. The direction of exploration is steered by the constraint
neurons. While many problems can be solved using only linear inhibitory
constraints, network performance on hard problems benefits significantly when
these negative constraints are implemented by non-linear multiplicative
inhibition. Overall, our results demonstrate the importance of instability
rather than stability in network computation, and also offer insight into the
computational role of dual inhibitory mechanisms in neural circuits.Comment: Accepted manuscript, in press, Neural Computation (2018
Budget Feasible Mechanism Design: From Prior-Free to Bayesian
Budget feasible mechanism design studies procurement combinatorial auctions
where the sellers have private costs to produce items, and the
buyer(auctioneer) aims to maximize a social valuation function on subsets of
items, under the budget constraint on the total payment. One of the most
important questions in the field is "which valuation domains admit truthful
budget feasible mechanisms with `small' approximations (compared to the social
optimum)?" Singer showed that additive and submodular functions have such
constant approximations. Recently, Dobzinski, Papadimitriou, and Singer gave an
O(log^2 n)-approximation mechanism for subadditive functions; they also
remarked that: "A fundamental question is whether, regardless of computational
constraints, a constant-factor budget feasible mechanism exists for subadditive
functions."
We address this question from two viewpoints: prior-free worst case analysis
and Bayesian analysis. For the prior-free framework, we use an LP that
describes the fractional cover of the valuation function; it is also connected
to the concept of approximate core in cooperative game theory. We provide an
O(I)-approximation mechanism for subadditive functions, via the worst case
integrality gap I of LP. This implies an O(log n)-approximation for subadditive
valuations, O(1)-approximation for XOS valuations, and for valuations with a
constant I. XOS valuations are an important class of functions that lie between
submodular and subadditive classes. We give another polynomial time O(log
n/loglog n) sub-logarithmic approximation mechanism for subadditive valuations.
For the Bayesian framework, we provide a constant approximation mechanism for
all subadditive functions, using the above prior-free mechanism for XOS
valuations as a subroutine. Our mechanism allows correlations in the
distribution of private information and is universally truthful.Comment: to appear in STOC 201
Acyclic Games and Iterative Voting
We consider iterative voting models and position them within the general
framework of acyclic games and game forms. More specifically, we classify
convergence results based on the underlying assumptions on the agent scheduler
(the order of players) and the action scheduler (which better-reply is played).
Our main technical result is providing a complete picture of conditions for
acyclicity in several variations of Plurality voting. In particular, we show
that (a) under the traditional lexicographic tie-breaking, the game converges
for any order of players under a weak restriction on voters' actions; and (b)
Plurality with randomized tie-breaking is not guaranteed to converge under
arbitrary agent schedulers, but from any initial state there is \emph{some}
path of better-replies to a Nash equilibrium. We thus show a first separation
between restricted-acyclicity and weak-acyclicity of game forms, thereby
settling an open question from [Kukushkin, IJGT 2011]. In addition, we refute
another conjecture regarding strongly-acyclic voting rules.Comment: some of the results appeared in preliminary versions of this paper:
Convergence to Equilibrium of Plurality Voting, Meir et al., AAAI 2010;
Strong and Weak Acyclicity in Iterative Voting, Meir, COMSOC 201
Consensus theories: an oriented survey
This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Consensus theories ; Arrowian results ; aggregation rules ; metric consensus rules ; median ; tournament solutions ; restricted domains ; lower valuations ; median semilattice ; complexity
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