187,397 research outputs found
Transferable Utility Games with Uncertainty
We introduce the concept of a TUU-game, a transferable utility game with uncertainty. In a TUU-game there is uncertainty regarding the payoffs of coalitions. One out of a finite number of states of nature materializes and conditional on the state, the players are involved in a particular transferable utility game. We consider the case without ex ante commitment possibilities and propose the Weak Sequential Core as a solution concept. We characterize the Weak Sequential Core and show that it is non-empty if all ex post TUgames are convex
Worst-Case Scenarios for Greedy, Centrality-Based Network Protection Strategies
The task of allocating preventative resources to a computer network in order
to protect against the spread of viruses is addressed. Virus spreading dynamics
are described by a linearized SIS model and protection is framed by an
optimization problem which maximizes the rate at which a virus in the network
is contained given finite resources. One approach to problems of this type
involve greedy heuristics which allocate all resources to the nodes with large
centrality measures. We address the worst case performance of such greedy
algorithms be constructing networks for which these greedy allocations are
arbitrarily inefficient. An example application is presented in which such a
worst case network might arise naturally and our results are verified
numerically by leveraging recent results which allow the exact optimal solution
to be computed via geometric programming
Student-Project Allocation with Preferences over Projects
We study the problem of allocating students to projects, where both students
and lecturers have preferences over projects, and both projects and lecturers
have capacities. In this context we seek a stable matching of students
to projects, which respects these preference and capacity constraints. Here,
the stability definition generalises the corresponding notion in the context of
the classical Hospitals / Residents problem. We show that stable matchings
can have different sizes, and the problem of finding a maximum cardinality
stable matching is NP-hard, though approximable within a factor of 2
An FPTAS for Bargaining Networks with Unequal Bargaining Powers
Bargaining networks model social or economic situations in which agents seek
to form the most lucrative partnership with another agent from among several
alternatives. There has been a flurry of recent research studying Nash
bargaining solutions (also called 'balanced outcomes') in bargaining networks,
so that we now know when such solutions exist, and also that they can be
computed efficiently, even by market agents behaving in a natural manner. In
this work we study a generalization of Nash bargaining, that models the
possibility of unequal 'bargaining powers'. This generalization was introduced
in [KB+10], where it was shown that the corresponding 'unequal division' (UD)
solutions exist if and only if Nash bargaining solutions exist, and also that a
certain local dynamics converges to UD solutions when they exist. However, the
bound on convergence time obtained for that dynamics was exponential in network
size for the unequal division case. This bound is tight, in the sense that
there exists instances on which the dynamics of [KB+10] converges only after
exponential time. Other approaches, such as the one of Kleinberg and Tardos, do
not generalize to the unsymmetrical case. Thus, the question of computational
tractability of UD solutions has remained open. In this paper, we provide an
FPTAS for the computation of UD solutions, when such solutions exist. On a
graph G=(V,E) with weights (i.e. pairwise profit opportunities) uniformly
bounded above by 1, our FPTAS finds an \eps-UD solution in time
poly(|V|,1/\eps). We also provide a fast local algorithm for finding \eps-UD
solution, providing further justification that a market can find such a
solution.Comment: 18 pages; Amin Saberi (Ed.): Internet and Network Economics - 6th
International Workshop, WINE 2010, Stanford, CA, USA, December 13-17, 2010.
Proceedings
On Orthogonal Band Allocation for Multi-User Multi-Band Cognitive Radio Networks: Stability Analysis
In this work, we study the problem of band allocation of buffered
secondary users (SUs) to primary bands licensed to (owned by)
buffered primary users (PUs). The bands are assigned to SUs in an orthogonal
(one-to-one) fashion such that neither band sharing nor multi-band allocations
are permitted. In order to study the stability region of the secondary network,
the optimization problem used to obtain the stability region's envelope
(closure) is established and is shown to be a linear program which can be
solved efficiently and reliably. We compare our orthogonal allocation system
with two typical low-complexity and intuitive band allocation systems. In one
system, each cognitive user chooses a band randomly in each time slot with some
assignment probability designed such that the system maintained stable, while
in the other system fixed (deterministic) band assignment is adopted throughout
the lifetime of the network. We derive the stability regions of these two
systems. We prove mathematically, as well as through numerical results, the
advantages of our proposed orthogonal system over the other two systems.Comment: Conditional Acceptance in IEEE Transactions on Communication
Perfect Simulation of Queues
In this paper we describe a perfect simulation algorithm for the stable
queue. Sigman (2011: Exact Simulation of the Stationary Distribution of
the FIFO M/G/c Queue. Journal of Applied Probability, 48A, 209--213) showed how
to build a dominated CFTP algorithm for perfect simulation of the super-stable
queue operating under First Come First Served discipline, with
dominating process provided by the corresponding queue (using Wolff's
sample path monotonicity, which applies when service durations are coupled in
order of initiation of service), and exploiting the fact that the workload
process for the queue remains the same under different queueing
disciplines, in particular under the Processor Sharing discipline, for which a
dynamic reversibility property holds. We generalize Sigman's construction to
the stable case by comparing the queue to a copy run under Random
Assignment. This allows us to produce a naive perfect simulation algorithm
based on running the dominating process back to the time it first empties. We
also construct a more efficient algorithm that uses sandwiching by lower and
upper processes constructed as coupled queues started respectively from
the empty state and the state of the queue under Random Assignment. A
careful analysis shows that appropriate ordering relationships can still be
maintained, so long as service durations continue to be coupled in order of
initiation of service. We summarize statistical checks of simulation output,
and demonstrate that the mean run-time is finite so long as the second moment
of the service duration distribution is finite.Comment: 28 pages, 5 figure
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