6,260 research outputs found
Applying Abstract Argumentation Theory to Cooperative Game Theory
We apply ideas from abstract argumentation theory to study cooperative game
theory. Building on Dung's results in his seminal paper, we further the
correspondence between Dung's four argumentation semantics and solution
concepts in cooperative game theory by showing that complete extensions (the
grounded extension) correspond to Roth's subsolutions (respectively, the
supercore). We then investigate the relationship between well-founded
argumentation frameworks and convex games, where in each case the semantics
(respectively, solution concepts) coincide; we prove that three-player convex
games do not in general have well-founded argumentation frameworks.Comment: 15 pages, 1 tabl
Solving stable matching problems using answer set programming
Since the introduction of the stable marriage problem (SMP) by Gale and
Shapley (1962), several variants and extensions have been investigated. While
this variety is useful to widen the application potential, each variant
requires a new algorithm for finding the stable matchings. To address this
issue, we propose an encoding of the SMP using answer set programming (ASP),
which can straightforwardly be adapted and extended to suit the needs of
specific applications. The use of ASP also means that we can take advantage of
highly efficient off-the-shelf solvers. To illustrate the flexibility of our
approach, we show how our ASP encoding naturally allows us to select optimal
stable matchings, i.e. matchings that are optimal according to some
user-specified criterion. To the best of our knowledge, our encoding offers the
first exact implementation to find sex-equal, minimum regret, egalitarian or
maximum cardinality stable matchings for SMP instances in which individuals may
designate unacceptable partners and ties between preferences are allowed.
This paper is under consideration in Theory and Practice of Logic Programming
(TPLP).Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP). arXiv admin note: substantial text overlap with arXiv:1302.725
Modeling Stable Matching Problems with Answer Set Programming
The Stable Marriage Problem (SMP) is a well-known matching problem first
introduced and solved by Gale and Shapley (1962). Several variants and
extensions to this problem have since been investigated to cover a wider set of
applications. Each time a new variant is considered, however, a new algorithm
needs to be developed and implemented. As an alternative, in this paper we
propose an encoding of the SMP using Answer Set Programming (ASP). Our encoding
can easily be extended and adapted to the needs of specific applications. As an
illustration we show how stable matchings can be found when individuals may
designate unacceptable partners and ties between preferences are allowed.
Subsequently, we show how our ASP based encoding naturally allows us to select
specific stable matchings which are optimal according to a given criterion.
Each time, we can rely on generic and efficient off-the-shelf answer set
solvers to find (optimal) stable matchings.Comment: 26 page
Stable Secretaries
We define and study a new variant of the secretary problem. Whereas in the
classic setting multiple secretaries compete for a single position, we study
the case where the secretaries arrive one at a time and are assigned, in an
on-line fashion, to one of multiple positions. Secretaries are ranked according
to talent, as in the original formulation, and in addition positions are ranked
according to attractiveness. To evaluate an online matching mechanism, we use
the notion of blocking pairs from stable matching theory: our goal is to
maximize the number of positions (or secretaries) that do not take part in a
blocking pair. This is compared with a stable matching in which no blocking
pair exists. We consider the case where secretaries arrive randomly, as well as
that of an adversarial arrival order, and provide corresponding upper and lower
bounds.Comment: Accepted for presentation at the 18th ACM conference on Economics and
Computation (EC 2017
New and simple algorithms for stable flow problems
Stable flows generalize the well-known concept of stable matchings to markets
in which transactions may involve several agents, forwarding flow from one to
another. An instance of the problem consists of a capacitated directed network,
in which vertices express their preferences over their incident edges. A
network flow is stable if there is no group of vertices that all could benefit
from rerouting the flow along a walk.
Fleiner established that a stable flow always exists by reducing it to the
stable allocation problem. We present an augmenting-path algorithm for
computing a stable flow, the first algorithm that achieves polynomial running
time for this problem without using stable allocation as a black-box
subroutine. We further consider the problem of finding a stable flow such that
the flow value on every edge is within a given interval. For this problem, we
present an elegant graph transformation and based on this, we devise a simple
and fast algorithm, which also can be used to find a solution to the stable
marriage problem with forced and forbidden edges.
Finally, we study the stable multicommodity flow model introduced by
Kir\'{a}ly and Pap. The original model is highly involved and allows for
commodity-dependent preference lists at the vertices and commodity-specific
edge capacities. We present several graph-based reductions that show
equivalence to a significantly simpler model. We further show that it is
NP-complete to decide whether an integral solution exists
A general framework for stable roommates problems using answer set programming
The Stable Roommates problem (SR) is characterized by the preferences of agents over other agents as roommates: each agent ranks all others in strict order of preference. A solution to SR is then a partition of the agents into pairs so that each pair shares a room, and there is no pair of agents that would block this matching (i.e., who prefers the other to their roommate in the matching). There are interesting variations of SR that are motivated by applications (e.g., the preference lists may be incomplete (SRI) and involve ties (SRTI)), and that try to find a more fair solution (e.g., Egalitarian SR). Unlike the Stable Marriage problem, every SR instance is not guaranteed to have a solution. For that reason, there are also variations of SR that try to find a good-enough solution (e.g., Almost SR). Most of these variations are NP-hard. We introduce a formal framework, called SRTI-ASP, utilizing the logic programming paradigm Answer Set Programming, that is provable and general enough to solve many of such variations of SR. Our empirical analysis shows that SRTI-ASP is also promising for applications
A general framework for stable roommates problems using answer set programming
The Stable Roommates problem (SR) is characterized by the preferences of agents over other agents as roommates: each agent ranks all others in strict order of preference. A solution to SR is then a partition of the agents into pairs so that each pair shares a room, and there is no pair of agents that would block this matching (i.e., who prefers the other to their roommate in the matching). There are interesting variations of SR that are motivated by applications (e.g., the preference lists may be incomplete (SRI) and involve ties (SRTI)), and that try to find a more fair solution (e.g., Egalitarian SR). Unlike the Stable Marriage problem, every SR instance is not guaranteed to have a solution. For that reason, there are also variations of SR that try to find a good-enough solution (e.g., Almost SR). Most of these variations are NP-hard. We introduce a formal framework, called SRTI-ASP, utilizing the logic programming paradigm Answer Set Programming, that is provable and general enough to solve many of such variations of SR. Our empirical analysis shows that SRTI-ASP is also promising for applications
Two theoretical interpretations of the dissonance between fertility intentions and behaviour
In the paper we outline two possible theoretical interpretations for the inconsistency often observed between fertility intentions and fertility behaviour. We draw on socio-psychological models of human behaviour which emphasise the role of normative-affective factors on decision-making processes. The first interpretation is based on the observation that family and fertility choices are gradually shifting from a zone where behaviour is normative regulated to a zone of normative indifference, where mere rational decision-making based on cost-benefit considerations is at work. The dissonance between fertility choices and declared intentions depends on the fact that the former are based on rational considerations, while the latter are still constrained by a normative familistic philosophy. The second interpretation assumes the existence of an interposing mechanism in the sequence expectations-behaviour. These mechanisms, as anxiety and avoidance dispositions, filter the passage from individual value orientations in the affective sphere to their actual behaviour. We base our argument on two sets of information. First, we use a survey which allows us to construct empirical indicators of psychological dispositions connected to expectations related to family and fertility behaviours (Abacus 1996, Italy). Second, we analyse 54 non-structured interviews conducted in Northern Italy, which give a detailed picture of the hypothesised mechanisms and suggest new directions for research.
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Proceedings ICPW'07: 2nd International Conference on the Pragmatic Web, 22-23 Oct. 2007, Tilburg: NL
Proceedings ICPW'07: 2nd International Conference on the Pragmatic Web, 22-23 Oct. 2007, Tilburg: N
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