30,348 research outputs found
Preference Elicitation in Matching Markets Via Interviews: A Study of Offline Benchmarks
The stable marriage problem and its extensions have been
extensively studied, with much of the work in the literature
assuming that agents fully know their own preferences over
alternatives. This assumption however is not always practical
(especially in large markets) and agents usually need
to go through some costly deliberation process in order to
learn their preferences. In this paper we assume that such
deliberations are carried out via interviews, where an interview
involves a man and a woman, each of whom learns
information about the other as a consequence. If everybody
interviews everyone else, then clearly agents can fully learn
their preferences. But interviews are costly, and we may
wish to minimize their use. It is often the case, especially
in practical settings, that due to correlation between agents’
preferences, it is unnecessary for all potential interviews to
be carried out in order to obtain a stable matching. Thus
the problem is to find a good strategy for interviews to be
carried out in order to minimize their use, whilst leading to a
stable matching. One way to evaluate the performance of an
interview strategy is to compare it against a na¨ıve algorithm
that conducts all interviews. We argue however that a more
meaningful comparison would be against an optimal offline
algorithm that has access to agents’ preference orderings under
complete information. We show that, unless P=NP, no
offline algorithm can compute the optimal interview strategy
in polynomial time. If we are additionally aiming for a
particular stable matching (perhaps one with certain desirable
properties), we provide restricted settings under which
efficient optimal offline algorithms exist
Monotone Preferences over Information
We consider preference relations over information that are monotone: more information is preferred to less. We prove that, if a preference relation on information about an uncountable set of states of nature is monotone, then it is not representable by a utility function
How to score alternatives when criteria are scored on an ordinal scale
International audienceWe address in this paper the problem of scoring alternatives when they are evaluated with respect to several criteria on a finite ordinal scale . We show that in general, the ordinal scale has to be refined or shrunk in order to be able to represent the preference of the decision maker by an aggregation operator belonging to the family of mean operators. The paper recalls previous theoretical results of the author giving necessary and sufficient conditions for a representation of preferences, and then focusses on describing practical algorithms and examples
Infinite sequential Nash equilibrium
In game theory, the concept of Nash equilibrium reflects the collective
stability of some individual strategies chosen by selfish agents. The concept
pertains to different classes of games, e.g. the sequential games, where the
agents play in turn. Two existing results are relevant here: first, all finite
such games have a Nash equilibrium (w.r.t. some given preferences) iff all the
given preferences are acyclic; second, all infinite such games have a Nash
equilibrium, if they involve two agents who compete for victory and if the
actual plays making a given agent win (and the opponent lose) form a
quasi-Borel set. This article generalises these two results via a single
result. More generally, under the axiomatic of Zermelo-Fraenkel plus the axiom
of dependent choice (ZF+DC), it proves a transfer theorem for infinite
sequential games: if all two-agent win-lose games that are built using a
well-behaved class of sets have a Nash equilibrium, then all multi-agent
multi-outcome games that are built using the same well-behaved class of sets
have a Nash equilibrium, provided that the inverse relations of the agents'
preferences are strictly well-founded.Comment: 14 pages, will be published in LMCS-2011-65
Arrovian juntas
This article explicitly constructs and classifies all arrovian voting systems
on three or more alternatives. If we demand orderings to be complete, we have,
of course, Arrow's classical dictator theorem, and a closer look reveals the
classification of all such voting systems as dictatorial hierarchies. If we
leave the traditional realm of complete orderings, the picture changes. Here we
consider the more general setting where alternatives may be incomparable, that
is, we allow orderings that are reflexive and transitive but not necessarily
complete. Instead of a dictator we exhibit a junta whose internal hierarchy or
coalition structure can be surprisingly rich. We give an explicit description
of all such voting systems, generalizing and unifying various previous results.Comment: 22 pages, 1 figur
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